motion-corrected tracer kinetic mapping using mri

Abstract

This document discloses a medical system (100, 300, 500) including a memory (110) storing machine-executable instructions (120) and a magnetic resonance reconstruction module (122). The magnetic resonance reconstruction module is configured to reconstruct a motion-corrected tracer kinetic map (126) based on measured k-space data (124). The measured k-space data is undersampled, wherein the measured k-space data is T1-weighted. The measured k-space data is dynamic contrast-enhanced k-space data. The medical system also includes a processor (104) configured to control the medical system. The execution of the machine-executable instructions causes the processor to: receive (200) the measured k-space data; and reconstruct (202) the motion-corrected tracer kinetic map by inputting the measured k-space data into the magnetic resonance reconstruction module. The magnetic resonance reconstruction module (122) is configured to reconstruct the motion-corrected tracer kinetic map into a direct model-based reconstruction based on the measured k-space data (124).

Description

Technical Field

[0001] This invention relates to magnetic resonance imaging, and more specifically to dynamic contrast-enhanced magnetic resonance imaging. Background Technology

[0002] As part of the process of generating images of a patient's body, a large static magnetic field is used by a magnetic resonance imaging (MRI) scanner to align the nuclear spins of atoms. This large static magnetic field is called the B0 field or main magnetic field. MRI can be used to spatially measure various quantities or properties of an object. In some MRI techniques, a contrast agent such as gadolinium can be injected into the object, which affects the T1 relaxation time. Measurements taken over time can be used to determine the delivery of the contrast agent through the object. A so-called tracer kinetic model can then be fitted to the delivery of the object to determine amounts such as perfusion.

[0003] The journal article Guo et al. (2017) "Direct estimation of tracer-kinetic parametermaps from highly undersampled brain dynamic contrast enhanced MRI" (Magn. Reson. Med., 78: 1566-1578. doi: 10.1002 / mrm.26540) discloses a reconstruction method involving solving a nonlinear least squares optimization problem that involves explicitly using a fully forward-looking model to transform the parameter maps to the (k,t) space using a Patlak TK model. The proposed scheme is compared with indirect methods that create intermediate images through parallel imaging and compressed sensing prior to TK modeling. Summary of the Invention

[0004] The present invention provides medical systems, computer program products, and methods in the independent claims. Embodiments are given in the dependent claims.

[0005] The method discussed by Guo et al. is used for dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI) of the brain. When imaging the brain, the subject's head is directly constrained. The technique described by Guo et al. (2007) does not work for other DCE MRI techniques, such as first-pass perfusion cardiac CDE MRI or abdominal DCE MRI. Embodiments can provide means of generating tracer kinetics (TK) maps by providing motion correction. This can be accomplished, for example, in several different ways. In some embodiments, the optimization problem is modified to include additional terms to correct for subject motion. In other embodiments, a trained neural network can be trained to compensate for subject motion, such as breathing and / or cardiac motion. In yet another embodiment, motion-corrected k-space data is first computed using measured k-space data. Then, motion-corrected tracer kinetics maps are computed using the motion-corrected k-space data. Throughout this document, references to k-space data are understood to refer to k-space data sampled as a function of both position and time in k-space.

[0006] In one aspect, the present invention provides a medical system including a memory storing machine-executable instructions and a magnetic resonance reconstruction module. The magnetic resonance reconstruction module is configured to reconstruct a motion-corrected tracer kinetic map based on measured k-space data. The measured k-space data is undersampled. The measured k-space data is T1-weighted. The measured k-space data is dynamically contrast-enhanced k-space data.

[0007] As used herein, a medical system encompasses a workstation or computer configured to process medical imaging data and / or a system for acquiring such medical imaging data. For example, in one instance, the medical system could be a workstation. In another example, the medical system could be a combination of a magnetic resonance imaging system and a medical system.

[0008] In dynamic contrast-enhanced or DCE MRI, repeated measurements over a period of time can be used to determine DCE signal data, which can lead to changes in the D1 contrast of the measured MRI image. This DCE signal data can be converted into gadolinium concentration. Once the gadolinium concentration is determined as a function of time, it is possible to fit a tissue model that models the delivery of gadolinium through the subject. This tissue model is called a tracer kinetic plot. Various tracer kinetic plots exist. One common one is the Tofts model. In this model, there are fractional plasma volumes for voxel portions, and also fractional extravascular spaces. The delivery of gadolinium from fractional plasma volumes to the extracellular extravascular space can be used to measure perfusion. In cardiac DCE MRI, this measurement of perfusion can be a measure of the subject's health or well-being. The motion-corrected tracer kinetic plot used in this paper encompasses the parameters fitted to the model of contrast agent or gadolinium delivery.

[0009] The medical system also includes a processor configured to control the medical system. The execution of the machine-executable instructions causes the processor to receive the measured k-space data. The measured k-space data can be retrieved, for example, from a memory storage device or via a network. In other examples, the machine-executable instructions can control a medical imaging system or a magnetic resonance imaging system to acquire the measured k-space data. The execution of the machine-executable instructions also causes the processor to reconstruct the motion-corrected tracer kinetic map by inputting the measured k-space data into the magnetic resonance reconstruction module. This embodiment can be advantageous because the k-space data has been undersampled. Undersampling means that the k-space data does not satisfy the Nyquist criterion.

[0010] However, in repeated measurements of the k-space data that constitute the measurement, redundancy may exist in the measurement that allows for undersampling of the k-space data. The measured k-space data can, for example, be used directly to calculate a motion-corrected tracer kinetic map based on the magnetic resonance reconstruction module. This can provide an increased rate of acquisition of the measured k-space data and an improved quality or accuracy of the motion-corrected tracer kinetic map.

[0011] In another embodiment, the magnetic resonance reconstruction module is configured to reconstruct the motion-corrected tracer kinetic map into a direct model-based reconstruction based on the measured k-space data.

[0012] In another embodiment, the magnetic resonance reconstruction module is configured to solve the motion-corrected tracer kinetics map as an optimization problem. The optimization problem includes a motion compensation regularization term. This embodiment can be advantageous because intermediate steps typically used to compute the tracer kinetics map can be skipped. The use of an optimization problem allows for a higher degree of undersampling of the k-space data. This can, for example, allow for faster acquisition of measured k-space data. The use of the regularization term enables greater motion compensation.

[0013] In another embodiment, the optimization problem is a single optimization problem of directly solving the motion-corrected tracer kinetic map from the measured k-space data.

[0014] In another embodiment, the motion compensation regularization term is formulated based on a deformed graph of the motion-corrected tracer kinetics.

[0015] In another embodiment, the deformation diagram has time and space dependencies.

[0016] In another embodiment, the motion compensation regularization term is formulated as a storage function that depends on the deformation graph.

[0017] In another embodiment, the motion compensation regularization term is formulated as a hyperelastic material model that depends on the deformation graph.

[0018] In another embodiment, the motion compensation regularization term is formulated as a curvature-based regularization term dependent on the deformation graph.

[0019] In another embodiment, the motion compensation regularization term is formulated as a free-form deformation model using a cubic B-spline model that depends on the deformation graph.

[0020] In another embodiment, the motion compensation regularization term is formulated as an affine transformation model that depends on the deformation graph.

[0021] In another embodiment, the motion compensation regularization term is a non-rigid body motion compensation regularization term.

[0022] In another embodiment, the motion compensation regularization term is a rigid body motion compensation regularization term.

[0023] Motion compensation regularization terms can be, for example, rigid body, affine, or non-rigid body motion compensation regularization terms. This can be implemented in various ways. For rigid body transformations, it can result in a phase shift in the measured k-space data. In other paradigms, the energy storage function of a hyperelastic material, a curvature-based regularization term, or even a free-form deformation model using a cubic B-spline model can be used. This enables non-rigid body motion compensation for motion-corrected tracer kinetic plots.

[0024] In another embodiment, the optimization problem is formulated as minimizing the motion compensation regularization term plus the norm of the difference between the measured k-space data and the k-space model configured to map the undersampled k-space data. This embodiment can be advantageous because it provides a means of calculating a motion-corrected tracer kinetic map from the measured k-space data without intermediate steps. This reuses the redundancy of the k-space data measurements and also allows the measured k-space data to be undersampled more extensively.

[0025] In another embodiment, the norm is the L2 norm. The use of the L2 norm has been shown to work appropriately in numerical methods. However, other numerical norms may also be used.

[0026] In another embodiment, the optimization problem includes the medical system according to claim 2 or 3, wherein the optimization problem includes:

[0027]

[0028] Where r is the spatial location, t is the time, TK(r) is a term of the tracer kinetics graph, R(M(r,t)) is the motion compensation regularization term, d(k,t) is the measured k-space data, M(r,t) is the deformation graph, f(TK(r),M(r,t)) is the forward model for k-space data given TK(r) and M(r,t), and the norm is the mathematical norm.

[0029] The term TK is commonly used to refer to tracer kinetic diagrams. The term norm is used to refer to a general or common norm as a mathematical norm. In some instances, the norm can be the L2 norm.

[0030] Different tracer kinetic models can replace the above TK(r), for example, the Patlak TK model can exist in the following equation:

[0031] In the above example, the L2 norm is also optionally substituted for the generalized norm. Furthermore, based on the hyperelastic regularization term R... hyper The problem allows for large and smooth deformations while maintaining elastic behavior. Other models can be used, such as curvature-based regularization, affine transformations, and free deformation (FFD) parameterized using a cubic B-spline model, and others can also be employed. The problem can be solved, for example, using an alternating minimization scheme.

[0032] The above embodiments and descriptions can be modified to formulate a single optimization problem without regularization terms. This provides additional embodiments. In one such embodiment, the single optimization problem becomes...

[0033]

[0034] The deformation diagram M(r,t) still exists and is able to correct the motion of the object. The other terms in the above equation are as described above.

[0035] In another similar embodiment, the optimization problem is formulated as minimizing the norm of the difference between the measured k-space data and a k-space model configured to map the motion-corrected tracer kinetics plot to undersampled k-space data. This embodiment also has the advantage of performing motion correction without a regularization term.

[0036] In another embodiment, the magnetic resonance reconstruction module is a neural network. The neural network is trained to output the motion-corrected tracer kinetic map in response to the input k-space data. This embodiment can be advantageous because measuring k-space data and then directly receiving the motion-corrected tracer kinetic map can be very efficient.

[0037] In another embodiment, the neural network can be trained using k-space data for a specific volume of interest. For example, in generating a motion-corrected tracer kinetic map for a cardiac condition, the training data could be k-space data of the cardiac region and the motion-corrected tracer kinetic map.

[0038] In another embodiment, the neural network is trained using a motion-corrected tracer kinetic map paired with simulated motion-damped k-space data. For example, various means can be used to obtain the motion-corrected tracer kinetic map. For instance, the motion-corrected tracer kinetic map can be determined using fully sampled measured k-space data. Motion correction can then be performed using imaging techniques such as deformable or non-deformable mappings between a series of images. Regardless of how the motion-corrected tracer kinetic map is reconstructed, the equations can be worked backward to create simulated motion-corrected k-space data. For example, k-space data for a fully sampled motion-corrected tracer kinetic map can be computed. A subset of this data can be considered as undersampled k-space data. Motion artifacts can then be artificially added to this k-space data.

[0039] In another embodiment, the execution of the machine-executable instructions further causes the processor to use the measured k-space data to calculate the motion-corrected k-space data. The tracer kinetics map is calculated by inputting the motion-corrected k-space data into the magnetic resonance reconstruction module. In this embodiment, the measured k-space data is motion-corrected before it is inserted. This can, for example, be used to correct certain types of motion. For example, rigid body motion of an object can be compensated in the k-space data by changing the phase of the measured k-space data. This can be implemented, for example, in different ways. The measured k-space data can be self-navigating k-space data. For example, k-space measurements can be focused on a central region, and this data alone may be sufficient to detect rigid body transformations of the object. In another example, subsequent acquisition of the measured k-space data can be used to generate individual images, which are then used to calculate translations used to correct the phase in k-space.

[0040] Other methods may include the use of image navigators (such as two-dimensional navigators that use a magnetic resonance imaging system to acquire images) and external navigators (such as breathing bellows, cameras, or breathing ties).

[0041] In another embodiment, the magnetic resonance reconstruction module is configured to solve the motion-corrected tracer kinetics map as an optimization problem or using a trained convolutional neural network. This embodiment can be similar to the previously mentioned embodiments, but motion correction can be performed before the k-space data is input into the magnetic resonance reconstruction module.

[0042] In another embodiment, the tracer kinetic map is a mapping of any of the following: relative extracellular volume, intravascular plasma volume, plasma flow rate, permeability-surface area product, extracellular space outside blood vessels, inflow mass transfer rate of contrast agents such as gadolinium, myocardial blood flow, and combinations thereof.

[0043] In another embodiment, the measured k-space data is first-pass perfusion cardiac k-space data. This embodiment can be advantageous because undersampling can help reduce the importance of motion artifacts. Additionally, respiratory motion and cardiac motion may be present during first-pass perfusion cardiac MRI. Motion compensation can help improve the quality of the motion-corrected tracer kinetic map.

[0044] In another embodiment, the measured k-space data is abdominal dynamic contrast-enhanced k-space data. This embodiment can be advantageous because motion correction can help compensate for abdominal movements caused by the subject's breathing.

[0045] In another embodiment, the measured k-space data is multi-coil k-space data. For example, multiple receiving coils may be present for receiving the measured k-space data. This can be particularly advantageous because when multi-coil k-space data is acquired, it is typically undersampled and then reconstructed using something similar to the SENSE magnetic resonance imaging protocol. The magnetic resonance reconstruction module can be configured to use the k-space data and combine it using coil sensitivity.

[0046] In another embodiment, the measured k-space data is undersampled with a factor of at least 5.

[0047] In another embodiment, the measured k-space data is undersampled by a factor of at least 10.

[0048] In another embodiment, the measured k-space data is undersampled by a factor of more than 20.

[0049] In another embodiment, the measured k-space data is undersampled with a factor of at least 30.

[0050] In another embodiment, the measured k-space data is undersampled with a factor of at least 40.

[0051] In another embodiment, the measured k-space data is undersampled with a factor of at least 50.

[0052] In another embodiment, the measured k-space data is undersampled with a factor of at least 60.

[0053] In another embodiment, the measured k-space data is undersampled with a factor of less than 70.

[0054] In another embodiment, the measured k-space data is undersampled with a factor of at least 80.

[0055] In another embodiment, the medical system further includes a magnetic resonance imaging (MRI) system configured to acquire the measured k-space data from an imaging region. The memory also contains pulse sequence commands. These pulse sequence commands are configured to acquire the measured k-space data according to a first-pass perfusion cardiac MRI protocol or an abdominal dynamic contrast-enhanced MRI protocol. The execution of the machine-executable instructions further enables the processor to use the pulse sequence commands to control the MRI system to acquire the measured k-space data. This embodiment can be advantageous because the medical system can provide motion-corrected tracer kinetic maps with reduced motion artifacts.

[0056] In another embodiment, the pulse sequence command is configured to acquire k-space data using a self-navigating k-space sampling mode. For example, the self-navigating k-space sampling mode could be a so-called star stack. In a star stack, a core k-space sampling mode rotates in k-space. In each measurement, the central region of k-space is sampled, and the central k-space data can be used to perform self-navigation.

[0057] In another aspect, the present invention provides a method for operating a medical system. The method includes receiving measured k-space data. The method further includes reconstructing a motion-corrected tracer kinetic map by inputting the measured k-space data into a magnetic resonance reconstruction module. The magnetic resonance reconstruction module is configured to reconstruct the motion-corrected tracer kinetic map based on the measured k-space data. The measured k-space data is undersampled. The measured k-space data is T1-weighted. The measured k-space data is dynamic contrast-enhanced k-space data.

[0058] In another aspect, the present invention provides a computer program product comprising machine-executable instructions for execution by a processor controlling a medical system. The machine-executable instructions include a magnetic resonance reconstruction module. The magnetic resonance reconstruction module is configured to reconstruct a motion-corrected tracer kinetic map based on measured k-space data. The measured k-space data is undersampled. The measured k-space data is T1-weighted. The measured k-space data is dynamically contrast-enhanced k-space data. Execution of the machine-executable instructions causes the processor to receive the measured k-space data. Execution of the machine-executable instructions also causes the processor to reconstruct the motion-corrected tracer kinetic map by inputting the measured k-space data into the magnetic resonance reconstruction module.

[0059] It should be understood that one or more of the above embodiments of the present invention can be combined, as long as the combined embodiments are not mutually exclusive.

[0060] As those skilled in the art will recognize, various aspects of the present invention can be implemented as apparatus, method, or computer program product. Accordingly, various aspects of the present invention can take the form of a completely hardware embodiment, a completely software embodiment (including firmware, resident software, microcode, etc.), or an embodiment combining software and hardware aspects (all of which may be referred to herein as "circuit," "module," or "system" in general). Furthermore, various aspects of the present invention can take the form of a computer program product implemented in one or more computer-readable media having computer-executable code implemented thereon.

[0061] Any combination of one or more computer-readable media can be used. The computer-readable media can be a computer-readable signal medium or a computer-readable storage medium. As used herein, "computer-readable storage medium" encompasses any tangible storage medium capable of storing instructions executable by a processor of a computing device. A computer-readable storage medium may be referred to as a computer-readable non-transitory storage medium. A computer-readable storage medium may also be referred to as a tangible computer-readable medium. In some embodiments, a computer-readable storage medium may also be capable of storing data accessible by a processor of a computing device. Examples of computer-readable storage media include, but are not limited to: floppy disks, magnetic hard disk drives, solid-state drives, flash memory, USB thumb drives, random access memory (RAM), read-only memory (ROM), optical discs, magneto-optical discs, and processor register files. Examples of optical discs include compact discs (CDs) and digital universal discs (DVDs), such as CD-ROMs, CD-RWs, CD-Rs, DVD-ROMs, DVD-RWs, or DVD-R discs. The term computer-readable storage medium also refers to various types of recording media accessible by a computer device via a network or communication link. For example, data can be retrieved on a modem, the Internet, or a local area network. Computer-executable code implemented on a computer-readable medium may be transmitted using any suitable medium, including but not limited to wireless, wired, fiber optic cable, RF, or any suitable combination thereof.

[0062] Computer-readable signal media may include propagated data signals having computer-executable code implemented therein, for example, in baseband or as a carrier wave. Such propagated signals may take any variety of forms, including but not limited to electromagnetic, optical, or any suitable combination thereof. A computer-readable signal medium may be any computer-readable medium that is not a computer-readable storage medium and is capable of conveying, propagating, or transmitting a program used by or in conjunction with an instruction execution system, apparatus, or device.

[0063] "Computer memory" or "memory" is an example of a computer-readable storage medium. Computer memory is any memory that can be directly accessed by a processor. "Computer storage device" or "storage device" is another example of a computer-readable storage medium. A computer storage device is any non-volatile computer-readable storage medium. In some embodiments, a computer storage device may also be computer memory, or vice versa.

[0064] As used herein, the term "processor" encompasses electronic components capable of executing programs or machine-executable instructions or computer-executable code. References to computing devices including "processor" should be interpreted as capable of containing more than one processor or processing core. A processor may, for example, be a multi-core processor. A processor may also refer to a collection of processors within a single computer system or distributed across multiple computer systems. The term computing device should also be interpreted as capable of referring to a collection or network of computing devices, each comprising one or more processors. Computer-executable code can be executed by multiple processors, which may be within the same computing device or even distributed across multiple computing devices.

[0065] Computer executable code may include machine-executable instructions or programs that instruct a processor to perform aspects of the present invention. Computer executable code for performing operations related to aspects of the present invention may be written in any combination of one or more programming languages ​​and compiled into machine-executable instructions, including object-oriented programming languages ​​such as Java, Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" programming language or similar programming languages. In some instances, the computer executable code may be in the form of a high-level language or in a pre-compiled form and used in conjunction with an interpreter that generates machine-executable instructions at runtime.

[0066] The computer-executable code may be executed entirely on the user's computer, partially on the user's computer (as a standalone software package), partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the latter case, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., via the Internet provided by an Internet service provider).

[0067] Aspects of the invention are described with reference to flowchart illustrations, diagrams, and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It should be understood that, when applicable, each block or portion of a flowchart illustration, diagram, and / or block diagram can be implemented by computer program instructions in the form of computer-executable code. It should also be understood that combinations of blocks from different flowchart illustrations, diagrams, and / or block diagrams can be combined when not mutually exclusive. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus that produces the machine, such that the instructions, executable via the processor of the computer or other programmable data processing apparatus, create units for implementing the functions / actions specified in the flowchart illustrations and / or one or more block diagram blocks.

[0068] These computer program instructions may also be stored in a computer-readable medium that can instruct a computer, other programmable data processing apparatus or other device to operate in a particular manner, such that the instructions stored in the computer-readable medium produce an article of writing that includes instructions that implement the functions / actions specified in flowcharts and / or one or more block diagrams.

[0069] The computer program instructions may also be loaded onto a computer, other programmable data processing apparatus or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device, thereby producing a computer-implemented process, such that the instructions, which execute on the computer or other programmable apparatus, provide a process for the function / action specified in the flowchart and / or one or more block diagram boxes.

[0070] As used herein, a "user interface" is an interface that allows a user or operator to interact with a computer or computer system. A "user interface" can also be referred to as a "human-machine interface device." A user interface can provide or receive information or data from an operator. A user interface enables input from an operator to be received by the computer and output from the computer to the user. In other words, the user interface allows an operator to control or manipulate the computer, and the interface allows the computer to indicate the effects of the operator's control or manipulation. The display of data or information on a monitor or graphical user interface is an example of providing information to an operator. The reception of data via a keyboard, mouse, trackball, touchpad, pointing stick, graphics tablet, joystick, game controller, webcam, headset, pedal, wired gloves, remote control, and accelerometer are all examples of user interface components that implement the reception of information or data from an operator.

[0071] As used herein, "hardware interface" encompasses the interface that enables a computer system's processor to interact with and / or control external computing devices and / or devices. A hardware interface can allow the processor to send control signals or instructions to external computing devices and / or devices. A hardware interface can also enable the processor to exchange data with external computing devices and / or devices. Examples of hardware interfaces include, but are not limited to: Universal Serial Bus (USB), IEEE 1394 port, parallel port, IEEE 1284 port, serial port, RS-232 port, IEEE-488 port, Bluetooth connectivity, wireless LAN connectivity, TCP / IP connectivity, Ethernet connectivity, control voltage interface, MIDI interface, analog input interface, and digital input interface.

[0072] As used herein, “display” or “display device” encompasses an output device or user interface suitable for displaying images or data. Displays can output visual, audio, and / or tactile data. Examples of displays include, but are not limited to: computer monitors, television screens, touchscreens, tactile electronic displays, Braille screens, cathode ray tubes (CRTs), memory tubes, bistable displays, electronic paper, vector displays, flat panel displays, vacuum fluorescent displays (VFs), light-emitting diode (LED) displays, electroluminescent displays (ELDs), plasma display panels (PDPs), liquid crystal displays (LCDs), organic light-emitting diode (OLED) displays, projectors, and head-mounted displays.

[0073] k-space data is defined in this paper as a measurement of radio frequency signals emitted by atomic spins, recorded by the antenna of a magnetic resonance imaging (MRI) device during a magnetic resonance imaging (MRI) scan. k-space data is an example of medical imaging data. MRI or MR images are defined in this paper as reconstructed two-dimensional or three-dimensional visualizations of anatomical data contained within MRI data. This visualization can be performed using a computer. Attached Figure Description

[0074] Preferred embodiments of the invention will be described below by way of example only, and with reference to the accompanying drawings, in which:

[0075] Figure 1 The diagram illustrates the medical system;

[0076] Figure 2 The operation is shown Figure 1 The methods of the medical system;

[0077] Figure 3 This illustration shows another example of a medical system;

[0078] Figure 4 The operation is shown Figure 1 The methods of the medical system;

[0079] Figure 5 This illustration shows another example of a medical system;

[0080] Figure 6 The operation is shown Figure 1 The methods of the medical system;

[0081] Figure 7 Several methods for calculating tracer kinetics are illustrated;

[0082] Figure 8 Several different algorithms for calculating tracer kinetic maps were compared;

[0083] Figure 9Several different algorithms for calculating tracer kinetic maps were also compared; and

[0084] Figure 10 Several different algorithms used to calculate tracer kinetic maps were also compared.

[0085] List of reference numerals

[0086] 100 Medical Systems

[0087] 102 Computer

[0088] 104 processor

[0089] 106 Hardware Interfaces

[0090] 108 User Interface

[0091] 110 Memory

[0092] 120 Machine-executable instructions

[0093] 122 Magnetic Resonance Reconstruction Module

[0094] 124 k-space data measured

[0095] 126. Motion-corrected tracer kinetics.

[0096] 200 Receive measurement of k-space data

[0097] 202 Motion-corrected tracer kinetics are reconstructed by inputting the measured k-space data into the magnetic resonance reconstruction module.

[0098] 300 Medical System

[0099] 302 Motion-corrected k-space data

[0100] 400 The tracer kinetics map is calculated by inputting motion-corrected k-space data into the magnetic resonance reconstruction module.

[0101] 500 Medical System

[0102] 502 Magnetic Resonance Imaging System

[0103] 504 magnet

[0104] 506 Magnet Chamber

[0105] 508 Imaging Area

[0106] 509 Field of View

[0107] 510 Magnetic Gradient Coil

[0108] 512 Magnetic Gradient Coil Power Supply

[0109] 514 RF coil

[0110] 516 transceiver

[0111] 518 objects

[0112] 520 Object Support

[0113] 530 Pulse Sequence Command

[0114] 600. A pulse sequence command is used to control the magnetic resonance imaging system to acquire measured k-space data.

[0115] 700 multi-coil (k,t) spatial data

[0116] 702 MR signal intensity s

[0117] 704 Contrast Agent Concentration

[0118] 706 Indirect Reconstruction

[0119] 708 arrows

[0120] 710 Direct Model-Based Reconstruction

[0121] 800 K Trans

[0122] 802 v p

[0123] 804 Full Sampling

[0124] 806 10x undersampling

[0125] 808 20x undersampling

[0126] 810 30x undersampling

[0127] 812 40x undersampling

[0128] 830 Indirect

[0129] 832 DIREQT

[0130] 834 DIREQT-TV900 Normalized Mean Square Error

[0131] 902 Correlation coefficient Detailed Implementation

[0132] Elements with similar numbers in these figures are either equivalent or perform the same function. If they are functionally equivalent, elements already discussed will not need to be discussed in later figures.

[0133] Figure 1 An embodiment of a medical system 100 is illustrated. The medical system 100 is shown as including a computer 102. The computer 102 includes a processor 104. The processor 104 is intended to represent one or more processing cores distributed among one or more computers. For example, the computer 102 may actually represent one or more computers connected via a network. The processor 104 is shown as being connected to a hardware interface 106. The hardware interface 106 may, for example, enable the processor 104 to communicate and / or control other components of the medical system 100. The processor 104 is also shown as being connected to an optional user interface 108. The processor 104 is also connected to a memory 110.

[0134] Memory 110 can be any combination of memory accessible to processor 104. This can include things such as main memory, cache memory, and non-volatile memory such as flash RAM, hard disk drives, or other storage devices. In some examples, memory 110 can be considered as a non-transitory computer-readable medium.

[0135] Memory 110 is also shown to contain machine-executable instructions 120. Machine-executable instructions 120 enable processor 104 to control other components of medical system 100 and perform basic data analysis and image processing techniques. Memory 110 is also shown to contain a magnetic resonance reconstruction module 122, which is also part of the machine-executable instructions 120. The magnetic resonance reconstruction module may be executable code that enables processor 104 to acquire measured k-space data and reconstruct a tracer kinetic map. Memory 110 is also shown to contain measured k-space data 124. Memory 110 is also shown to contain a motion-corrected tracer kinetic map 126, which is reconstructed by inputting the measured k-space data 124 into the magnetic resonance reconstruction module 122.

[0136] Figure 2 The illustrated operation is shown. Figure 1 The flowchart of the method for the medical system 100 is as follows: First, in step 200, measured k-space data 124 is received. Next, in step 202, a motion-corrected tracer kinetic map 126 is reconstructed by inputting the measured k-space data 124 into the magnetic resonance reconstruction module 122.

[0137] Figure 3 Another embodiment of the medical system 300 is illustrated. Figure 3 The medical system in China is similar to Figure 1 The medical system 100 depicted in the text. Figure 3The medical system 300 is modified such that instead of directly inputting the measured k-space data 124 into the magnetic resonance reconstruction module 122, the processor 104 uses machine-executable instructions 120 to first correct / calculate motion-corrected k-space data 302 based on the measured k-space data 124. Then, the motion-corrected k-space data 302 is input into the magnetic resonance reconstruction module 122, and a motion-corrected tracer kinetic map 126 is output. The measured k-space data 124 may, for example, have self-navigating k-space data, or there may be an external system signal for the motion phase of the measured object. Either of these can be used to calculate the motion-corrected k-space data 302 based on the measured k-space data 124. Specifically, rigid body transformations between the acquisition portions of the measured k-space data 124 can be corrected to phase changes of the measured k-space data 124 to calculate the motion-corrected k-space data 302.

[0138] Figure 4 The illustrated operation is shown. Figure 3 The flowchart of the method of medical system 300. First, perform as follows Figure 2 The illustrated step 200. Next, the method proceeds to step 400, where motion-corrected k-space data 302 is calculated using the measured k-space data 124. After performing step 400, the method proceeds to... Figure 2 Step 202 is illustrated in the figure.

[0139] Figure 5 Another embodiment of the medical system 500 is illustrated. The medical system 500 is similar to... Figure 1 The medical system 100 depicted includes a magnetic resonance imaging system 502 in addition to the medical system 500. Figure 3 The features of the medical system 300 described in the text can also be incorporated into Figure 5 The text describes 500 medical systems.

[0140] The magnetic resonance imaging system 502 includes a magnet 504. Magnet 504 is a superconducting cylindrical magnet with a bore 506 passing through it. It is also possible to use different types of magnets; for example, both split cylindrical magnets and so-called open magnets can be used. A split cylindrical magnet is similar to a standard cylindrical magnet, except that the cryostat has been split into two segments to allow for approach to the equiplanar plane of the magnet. This type of magnet can be used, for example, in conjunction with charged particle beam therapy. An open magnet has two magnet segments, one on top of the other, with a sufficiently large space between them to receive the object: the arrangement of the two segments is similar to the arrangement of Helmholtz coils. Open magnets are common because the object is less constrained. A series of superconducting coils are present inside the cryostat of the cylindrical magnet.

[0141] An imaging region 508 is located within the bore 506 of a cylindrical magnet 504, in which the magnetic field is sufficiently strong and homogeneous to perform magnetic resonance imaging. A field of view 509 is shown within the imaging region 508. Magnetic resonance data is typically acquired for the field of view 509. An object 518 is shown supported by an object support 520 such that at least a portion of the object 518 is situated within the imaging region 508 and the field of view 509.

[0142] Within the bore 506 of the magnet, there is also an assembly of magnetic field gradient coils 510, which are used to acquire preliminary magnetic resonance data for spatial encoding of the magnetic spins within the imaging region 508 of the magnet 504. The magnetic field gradient coils 510 are connected to a magnetic field gradient coil power supply 512. The magnetic field gradient coils 510 are intended to be representative. Typically, the magnetic field gradient coils 510 comprise three separate coil assemblies for spatial encoding in three orthogonal spatial directions. The magnetic field gradient coil power supply supplies current to the magnetic field gradient coils. The current supplied to the magnetic field gradient coils 510 is controlled according to time, and this current can be either slanted or pulsed.

[0143] Adjacent to the imaging region 508 is an RF coil 514, which is used to manipulate the orientation of magnetic spins within the imaging region 508 and to receive RF transmissions from spins also located within the imaging region 508. The RF antenna may comprise multiple coil elements. The RF antenna may also be referred to as a channel or antenna. The RF coil 514 is connected to an RF transceiver 516. The RF coil 514 and the RF transceiver 516 may be replaced by separate transmit and receive coils, and separate transmitters and receivers. It should be understood that the RF coil 514 and the RF transceiver 516 are representative. The RF coil 514 is also intended to represent a dedicated transmit antenna and a dedicated receive antenna. Similarly, the transceiver 516 may also represent a separate transmitter and receiver. The RF coil 514 may also have multiple receive / transmit elements, and the RF transceiver 516 may have multiple receive / transmit channels. For example, if a parallel imaging technique such as SENSE is performed, the RF coil 514 may have multiple coil elements.

[0144] Transceiver 516 and gradient controller 512 are shown as hardware interface 106 connected to computer system 102. Memory 110 is also shown as containing pulse sequence commands. Pulse sequence commands 530 are commands or data that can be converted into commands to control the magnetic resonance imaging system 502 to acquire k-space data 124.

[0145] The memory 110 is also shown to contain a pulse sequence command 530. The pulse sequence command 530 can be used by the processor 104 to control the magnetic resonance imaging system 502 to acquire measured k-space data 124.

[0146] Figure 6The illustrated operation is shown. Figure 5 The flowchart illustrates the method of the medical system 500. First, in step 600, the processor 104 uses pulse sequence commands 530 to control the medical system 502 to acquire measured k-space data 124. After executing step 600, the method proceeds to... Figure 2 Steps 200 and 202 are illustrated.

[0147] As a concrete example, first-pass perfusion cardiac magnetic resonance imaging (FPP-CMR) allows for the assessment of coronary artery disease. However, conventional FPP-CMR suffers from low spatial resolution, inadequate cardiac coverage, and requires prolonged breath-holding. Currently, perfusion abnormalities are typically identified visually by trained physicians. Recently, quantitative analysis of FPP-CMR has emerged as a more reliable and operator-independent method for identifying perfusion inadequacies. Typically, quantitative FPP-CMR first reconstructs individual dynamic images, which are then converted to contrast agent concentrations, and finally, tracer kinetic modeling is used to generate quantitative myocardial perfusion maps. Here, we propose a model-based FPP-CMR reconstruction method that combines image reconstruction and tracer kinetic modeling to better utilize redundancy in FPP-CMR data. We demonstrate that this synergistic approach enables very high undersampling rates at each time frame, and thus allows for significantly higher spatial resolution and coverage than conventional methods. Furthermore, our proposed method can be combined with respiratory motion correction and kt undersampling to improve myocardial perfusion quantification while substantially increasing patient comfort.

[0148] Coronary artery disease (CAD) is a leading cause of death worldwide. It is typically caused by atherosclerosis, which reduces blood flow to the heart (myocardial ischemia). Positron emission tomography (PET) is a non-invasive clinical reference for quantifying myocardial perfusion in patients with myocardial ischemia. However, first-pass perfusion cardiac magnetic imaging (FPP-CMR) is rapidly evolving into an important tool for detecting myocardial hypoperfusion. Compared to PET, it offers advantages such as higher spatial resolution, no radiation exposure, wider availability, and lower scan costs. However, FPP-CMR requires ultra-fast acquisition (to capture the first pass of the contrast agent blotting), ECG gating, and breath-holding techniques to minimize cardiac and respiratory motion, resulting in a trade-off between spatial resolution (~2.5 mm) and cardiac coverage (~3 slices). Diagnostic accuracy is also impaired by respiratory-induced motion artifacts (patients often cannot hold their breath) and false-positive defects due to dark edge artifacts. Furthermore, perfusion abnormalities are often visually identifiable, which has prognostic value dependent on the operator's level of training and experience.

[0149] The lack of reproducible and accurate results is a major factor limiting the widespread clinical adoption of FPP-CMR. Typically, quantitative FPP-CMR methods first involve reconstructing individual dynamic contrast-enhanced images, which are then converted into contrast agent concentrations, and finally, tracer kinetic (TK) modeling is used to generate TK parameter maps; these methods can be referred to as “indirect” methods.

[0150] Direct model-based parameter reconstruction has been used in few applications in PET and dynamic contrast-enhanced MR imaging to obtain TK parameter maps directly from acquired data.

[0151] This method demonstrates superior quantitative performance compared to conventional indirect quantitative methods. Furthermore, the direct model-based reconstruction approach reduces the dimensionality of the problem; that is, the image reconstruction problem is reduced to finding 2–4 TK parameter maps instead of ~60 time points per pixel. Therefore, this method provides accurate TK parameter maps while also achieving a very high acceleration factor by utilizing the redundancy of spatial information between time points. To date, compressed sensing (CS) and parallel imaging reconstruction methods have been used to accelerate FPP-CMR acquisition to ~8x and achieve higher spatial resolution.

[0152] In this work, a direct quantitative (DIREQT) FPP-CMR reconstruction framework was proposed to directly estimate quantitative myocardial perfusion maps from undersampled data. The proposed framework was evaluated on a digital FPP-CMR phantom and in patients with suspected cardiac CAD.

[0153] The terms DIREQT and DIREQT-TV refer to two different implementations of the magnetic resonance reconstruction module 122, which is formulated as an optimization problem.

[0154] Figure 7The illustration shows two different ways to calculate the motion-corrected tracer kinetic map 126 based on measured k-space data 124. In the conventional method, the measured k-space data 124 is first acquired in step 700. Next, multiple magnetic resonance signal and intensity images 702 are reconstructed from the measured k-space data 124. In the next step, the contrast agent concentration 704 is calculated. Finally, an indirect reconstruction 706 of the tracer kinetic map 126 is reconstructed from these images 704. In this example, multiple images are reconstructed in step 702. For this reason, it may be impossible to acquire undersampled k-space data. An alternative to this is to use a direct model-based reconstruction 710 using the magnetic resonance reconstruction module 122. In this method, the motion-corrected tracer kinetic map 126 is calculated directly from the measured k-space data 124. This can be performed in several different ways. In one approach, a trained convolutional neural network can be used. In another approach, an optimization problem can be established and then solved, which directly solves the motion-corrected tracer kinetic diagram 126 from the measured k-space data 124.

[0155] As mentioned above, Figure 7 The steps required in generating conventional indirect methods (700, 702, 704, 706) and the DIREQT forward model (710) are shown, which converts the Tk parameters into (multi-coil undersampling) FPP-CMR measurements (k-space data 124).

[0156] The proposed DIREQT method estimates the TK parameter map directly from measured FPP-CMR data. This is achieved by inverting the operations described below (by... Figure 7 The forward model is implemented as indicated by arrow 708 in the diagram.

[0157] The TK parameters are mapped to contrast agent concentrations. The Patlak model is used to estimate the C(r,t) contrast agent concentration over time:

[0158]

[0159] Figure 7 The diagram illustrates the indirect method and the flowchart of the proposed DIREQT reconstruction to obtain TK parameters from multi-coil (undersampled) data d. The indirect reconstruction comprises three steps (blue arrows): First, the 702FPP-CMR signal intensity image is estimated based on the acquired (k,t) spatial data d. Then, according to The contrast agent concentration C over time is estimated. The TK parameter map is then estimated based on C. In DIREQT reconstruction, the TK parameters are estimated directly from the (k,t) spatial data d (long red arrow) by solving the inverse problem using an iterative reconstruction scheme. The forward model used for the transformation from the TK parameter map to the (k,t) spatial data d is indicated by the small red arrow.

[0160] Where r∈(x,y) are the image domain spatial coordinates, and C AIF It is the arterial input function, K Trans and v p These are the TK parameters representing the contrast transfer coefficient and the plasma volume fraction, respectively. Parameter K Trans It is related to vascular permeability and blood flow.

[0161] Contrast agent concentration versus signal intensity. The contrast agent concentration C(r,t) changes T1 according to the following equation:

[0162] 1 / T1(r,t)=1 / T1(r,0)+γC(r,t),(2)

[0163] Where T1(r,0) is the pre-contrast T1, and γ is the contrast agent relaxation. Dynamic contrast-enhanced image series. The equation for the fast gradient echo signal prepared by saturation recovery is related to T1:

[0164]

[0165] in, Proportional to the equilibrium longitudinal magnetization, T S It is the saturation time, T R The repetition time is n, where n is the number of excitation pulses applied before the acquisition of the k-space center, and R1 = 1 / T1. It includes the flip angle α. Equation 3 above is different from Equation 2 by Guo et al.

[0166] Undersampled (k,t) spatial data d(k,t) and The following is relevant:

[0167]

[0168] Where, k∈(k x ,k y Let A(k,t) represent the k-space coordinates, A(k,t) be the (k,t)-space sampling trajectory, F be the Fourier transform, and S(r) be the coil sensitivity. Therefore, the DIREQT forward problem is given by the following equation:

[0169] d(k,t)=f(K Trans (r),v p (r)),(5)

[0170] Here, f is the forward model combining equations (1)-(4). Therefore, the TK parameter map can be estimated by solving the following optimization problem:

[0171]

[0172] If motion correction is performed in k-space, then Equation 6 can be modified so that d is replaced by b, where b is the k-space data after translational motion correction.

[0173] The spatial sparsity constraint on the TK parameter graph can be added to equation (6):

[0174]

[0175] in, It is a 2D spatial finite difference operator, where α and β are regularization parameters or any other sparsity constraint, such as wavelet sparsity constraint. The nonlinear inverse problem is solved using the finite memory BFGS quasi-Newton method.

[0176] To solve the indirect problem, the individual dynamic contrast-enhanced image can be reconstructed from undersampled (k,t) spatial data by solving the following optimization problem:

[0177]

[0178] in, It is a finite difference operator along the time dimension. Then, the change in concentration C(r,t) is derived from the signal intensity, and finally, the TK parameter map is obtained from C(r,t) by solving the inverse problems of equations (3) and (1), respectively.

[0179] The direct formulas above can be modified for motion compensation by altering equations 4 and 6 or equation 7.

[0180] Undersampled (k,t) spatial data d(k,t) and The following is relevant, replacing Equation 4:

[0181]

[0182] Where M(r,t) is the (non-rigid) motion field at each time frame t.

[0183] Regularization of M can be based on the storage energy function of hyperelastic materials (such as Saint Venant-Kirchhoff or Ogden materials). This leads to the following minimization problem to replace Equation 6 above:

[0184]

[0185] Where r is the spatial location, t is the time, TK(r) is a term of the tracer kinetic graph, R(M(r,t)) is the motion compensation regularization term, d(k,t) is the measured k-space data, M(r,t) is the deformation graph, f(TK(r),M(r,t)) is the forward model for k-space data given TK(r) and M(r,t), and the norm is the mathematical norm.

[0186] Based on the hyperelastic regularization term R hyper This problem allows for large and smooth deformations while maintaining elastic behavior. Other models can be used, such as curvature-based regularization, affine transformations, and free deformation (FFD) parameterized using a cubic B-spline model. The problem can also be solved using an alternating minimization scheme.

[0187] Similarly, Equation 7 can be reformulated as:

[0188]

[0189] Equations 10 and 11 can also be improved by removing the regularization term R(M(r,t)). and / or To modify this, the presence of the deformed graph M(r,t) still achieves motion correction. The presence of a regularization term in a single optimization problem contributes to motion correction. However, removing the regularization term allows for a faster solution to a single optimization problem. It is numerically less demanding. Therefore, removing the regularization term is a trade-off between how well motion is compensated for in terms of computational efficiency.

[0190] Fully sampled FPP-CMR data was generated using the MRXCAT digital phantom and the following parameters: Field of view (FOV): 320×320×80mm 3 Spatial resolution: 2×2mm 2 Slice thickness: 5mm; TS / TR / TE: 150.0 / 2.0 / 1.0ms; Flip angle: 15°; Contrast agent dosage: 0.075mmol / kg, 5.6L / mmol·s; 6 receiving coils; 32 time frames and population average C AIF A radial kt sampling strategy was used to undersample the acquisitions with factors of 10, 20, 30, and 40. Gaussian noise was added to each dataset to obtain a contrast-to-noise ratio (CNR) of 40. Six noise implementations were performed for each undersampling rate. DIREQT and indirect reconstructions were obtained from the undersampled datasets.

[0191] In vivo experiments were also performed. The remaining FPP-CMR full sampling acquisition was performed in one patient with suspected CAD using a dual bolus technique with gadobutrol (Gadovist; Bayer, Germany) at 0.0075 ± 0.075 mmol / kg and a 3T scanner (Achieva; Philips Healthcare). A saturated recovery type fast field echo (TFE) ECG trigger sequence was used to acquire single short-axis slices during free breathing using the following parameters: FOV: 320 × 320 mm. 2 Resolution: 2.8×2.8mm 2 Slice thickness: 10 mm, TS / TR / TE: 120.0 / 1.96 / 0.93 ms, flip angle: 15°, acquisition window: 224.3 ms, total acquisition time: 1 min 20 s, contrast agent relaxation rate: 5.0 L / mmol·s. 20x, 30x, and 40x undersampled datasets were generated using the same radial sampling strategy used in the simulation. Ci was located using a region of great interest plotted in the left ventricle. AIF Furthermore, the pre-contrast T1(r,0) is extracted from the T1 mapping sequence. In addition, the signal intensity is normalized to the pre-contrast signal.

[0192] To perform motion correction, the vendor's default reconstruction was initially used to reconstruct free-breathing FPP-CMR acquisitions. Dynamic images were used to estimate frame-by-frame translational motion by registering each frame to a moving average of its predecessor (±7 frames). Translational motion correction was then performed directly in k-space by applying linear phase shift. Finally, these motion-corrected datasets were reconstructed using indirect and DIREQT methods.

[0193] The value of adding spatial sparsity constraints to the TK parameter graph in the form of spatial total variation (TV) regularization (see Equation (7)) was also tested. For all methods, the regularization parameter was chosen empirically.

[0194] The TK parameter maps obtained using DIREQT and indirect methods were quantitatively evaluated relative to a reference (fully sampled) TK parameter map using normalized mean squared error (NMSE) and correlation coefficient (CC). Reconstruction was performed using MATLAB (MathWorks, USA) on an i7-86508@1.9GHz laptop with 32GB of memory.

[0195] Figure 8 Several different methods for calculating the motion-corrected tracer kinetics in Figure 126 are compared. In this example, two different quantities are calculated as part of Figure 126. There exists K. Trans 800 and v p802. Calculations are performed for fully sampled measurements 804, 10x undersampling 806, 20x undersampling 808, 30x undersampling 810, and 40x undersampling 812. Each of these is performed using three different algorithms. This is performed for the following: via Figure 7 Steps 700, 702, 704, and 706 illustrate the indirect method 830, and then the DIREQT 832 algorithm and the DIREQT-TV algorithm 834 are used. From Figure 8 It can be seen that both DIREQT-TV 834 and DIREQT832 perform well in calculating the value K even at high undersampling rates. Trans 800 and v p 802's outstanding work. Figure 8 DIREQT reconstructions with and without TV regularization, as well as reference and indirect reconstructions obtained from simulated undersampled data, are shown. For the indirect method, the image quality of the TK map at 10x acceleration is comparable to the reference image. At higher acceleration rates, the quality of the TK parameter map deteriorates rapidly, and spurious underperfusion becomes visible. In contrast, the overall image quality of the TK parameter map obtained using DIREQT is superior to the indirect method at all undersampling levels. However, at high acceleration rates, the DIREQT problem becomes ill-posed, leading to noise amplification. In these instances, regularization strategies can be employed to stabilize the solution. Figure 8 It is shown that TV regularization helps reduce noise amplification under high acceleration and also improves the convergence rate.

[0196] Figure 9 The K values ​​for the indirect algorithm 830, DIREQT algorithm 832, and DIREQT-TV algorithm 834 are shown. Trans 800 and v p The normalized mean square error (MSE) and correlation coefficient (CQC) between the reference image (802) and the TK plot are 900 and 902, respectively. Figure 9 Quantitative results of TK parameter reconstruction are presented. The highest CC value and lowest NMSE value were achieved using the proposed DIREQT method, indicating better consistency with the reference image.

[0197] Figure 10 The digital phantom K is shown using an indirect method, the proposed DIREQT, and DIREQT with TV regularization (DIREQT-TV) from undersampled data at 10x, 20x, 30x, and 40x. Trans and v p Reconstruction. A reference image is shown for comparison. The proposed DIREQT generates high-quality TK maps even at very high undersampling rates.

[0198] Figure 10The diagram illustrates K obtained from measurement 804 (full sampling), measurement 808 (20x undersampling), measurement 810 (30x undersampling), and measurement 812 (40x undersampling) of patient data. Trans The differences between the reconstructed indirect 830 algorithm and the DREQT 832 algorithm. Finally, Figure 10 TK parameter plots estimated from fully sampled and undersampled patient data using DirectQT are shown. Note that FPP-CMR data were acquired without breath-holding to improve patient comfort and minimize respiratory motion artifacts that can significantly affect quantitative results. The proposed method produces good results even at high acceleration rates. The total reconstruction times for the indirect and DIREQT methods are ~290 s and ~185 s, respectively.

[0199] The Patlak model was chosen in this work because it provides comparable results to other TK models commonly used in FPP-CMR, such as the Fermi and two-compartment models, and has the advantage of being linearizable, which simplifies computation. However, comparisons between different TK models, including the blood tissue exchange (BTEX) model, will be a subject of future research. Furthermore, other regularization strategies can be employed, which could further increase the robustness of the proposed method to noise, thus further accelerating its development. In future studies, the DIREQT method will be evaluated using prospective undersampled acquisitions in a large cohort of patients with suspected CAD. These studies will also aim to achieve significantly higher spatial resolution and coverage, and therefore greater diagnostic accuracy.

[0200] Various techniques can be used for kt sampling and to provide dynamic acquisition schemes. Cardiac dynamic (parallel) images have high spatial-temporal correlation and redundancy because the background is static and the dynamic regions (or contrast changes) are relatively small.

[0201] To leverage the spatial-temporal correlation and redundancy of the entire dynamic FPP-CMR series, and thus achieve high incoherence, dynamic undersampling patterns can be used, i.e., different k-space undersampling patterns at each time point t. These kt-sampling trajectories acquire data in a manner that minimizes signal overlap. Therefore, the resulting aliasing artifacts are incoherently added together. This contrasts with the more standard approach of individually acquiring fully sampled, partially Fourier, or parallel imaging acceleration FPP-CMR datasets at each time frame. DIREQT also works with this standard approach, but can achieve higher acceleration using the kt-sampling strategy.

[0202] This can be achieved, for example, by using Cartesian or non-Cartesian trajectories with spiral or radial ordering and golden angle or tiny golden angle increments, or with non-repeating Poisson disk sampling trajectories. Sampling can have a higher density at the center of k-space, but this is not necessary.

[0203] DIREQT also does not require training data or profiles, such as, for example, kt SENSE and kt PCA methods. However, DIREQT can be used in combination with these types of techniques. DIREQT can also be combined with other FPP-CMR acquisition strategies, including simultaneous multi-slice imaging.

[0204] In summary, the spatial and temporal correlation of FPP-CMR dynamic frames facilitates the recovery of TK parameter maps. The use of kt trajectories with DIREQT allows for a significant reduction in the amount of data required to obtain high-quality TK parameter maps, and further allows for improved spatial and temporal resolution.

[0205] Respiratory motion and cardiac contraction degrade FPP-CMR image quality. These rigid and non-rigid deformations limit the quantitative accuracy of FPP-CMR. Therefore, to obtain accurate quantitative maps, motion compensation must be applied to the first-pass data to minimize the resulting artifacts. The proposed DIREQT method can be combined with motion correction techniques to provide accurate quantitative maps from highly accelerated free breathing and / or continuously acquired data.

[0206] Several methods can be used to minimize respiratory and cardiac motion. For example, the most common strategies use ECG triggering to freeze cardiac motion and breath-holding to reduce respiratory motion. Alternatively, self-navigation techniques can be used to extract motion information directly from data or assisted acquisition. This motion information can be used retrospectively to correct the acquired data. For example, translational motion correction can be performed directly in k-space by applying linear phase shift. Alternatively, data binning can be performed to separate the data into different respiratory motion states and / or cardiac phases. Furthermore, affine or non-rigid body motion can be estimated and corrected iteratively. Thus, the framework can be formulated as jointly estimating motion and a motion-corrected quantitative map directly from FPP-CMR data. Furthermore, the problem can also be formulated as follows: the arterial input function can be jointly estimated along with the TK parameter map and motion. Population AIF can be used as an initial estimate.

[0207] Deep learning can also be used to reconstruct motion-corrected tracer kinetic maps. 3D volumetric DIREQT reconstruction can potentially require long computation times. A potential solution to accelerate reconstruction time is to use deep learning methods to directly estimate the TK parameter map from undersampled FPP-CMR data (DIREQT-NET). One of the main advantages of deep learning-based reconstruction techniques is computational efficiency, enabling real-time applications.

[0208] One approach to solving equation (5) using deep learning is to directly learn the nonlinear mapping between the undersampled k-space data d or the undersampled reconstruction with aliased zero-padding using a deep neural network (e.g., a convolutional neural network, CNN) and the fully sampled TK parameter map. Therefore, the training step involves pairs of the undersampled k-space (or image) and the desired standard data TK parameter map. The reconstruction can then be trained end-to-end, where the TK parameter map is reconstructed from the undersampled data using the network and compared with the standard data.

[0209] The trained CNN can then be used to generate artifact-free TK parameter maps from undersampled FPP-CMR data. For very high speedup (where regularization can be used to stabilize DIREQT reconstruction), prior information or regularization is implicitly learned from the undersampled data (or images). Therefore, these do not need to be specified during training. Alternatively, a deep residual learning strategy can be used, in which the network learns a residual parameter map (between the corrupted TK map and the standard data TK map), which has a sparser and simpler representation than the parameter map. Thus, the network is trained to learn the mapping between undersampled k-space data (or images) and the TK parameter map, and outputs an estimate of the residual map. If k-space is the input data, the neural network can include fully connected layers following a CNN. The primary function of the fully connected layers is to learn a nonlinear mapping between k-space and the image domain. Alternatively, an unfolded iterative network can be used, which forces the reconstruction to be consistent with the k-space data.

[0210] Several loss functions can be used to train deep neural networks. A popular choice is the mean squared error between the TK parameter graph estimate and the standard data (or residuals). A forward physical model loss function between the input data and the model-generated data can also be included (Equation 5).

[0211] If standard data is available, the network can be trained in an end-to-end manner. However, acquiring fully sampled 2D high-resolution or 3D whole-heart FPP-CMR data may not be feasible. Therefore, if standard data images are unavailable, unsupervised deep learning methods can be used to jointly solve for the CNN weights and the reconstructed training set parameter map.

[0212] CNN weights can be referred to as weighting factors for CNNs or other types of neural networks.

[0213] Deep learning typically requires large datasets for training, which are often unavailable in FPP-CMR. However, it is still possible to use data augmentation techniques to train the network, which can be used to increase the amount of data and prevent overfitting.

[0214] Other deep neural networks besides CNNs can be used in DIREQT-NET, such as recurrent neural networks, (recurrent) generative adversarial networks, Bayesian neural networks, ADMM-Net, etc.

[0215] The use of Bayesian neural networks can be beneficial because it can additionally provide uncertainty maps, which can be useful in evaluating the accuracy of motion-corrected tracer kinetic maps.

[0216] Although the invention has been described and illustrated in detail in the accompanying drawings and the foregoing description, such description and illustration are to be regarded as illustrative or exemplary rather than restrictive; the invention is not limited to the disclosed embodiments.

[0217] Those skilled in the art, through studying the accompanying drawings, description, and claims, will be able to understand and implement other variations of the disclosed embodiments in practicing the claimed invention. In the claims, the word "comprising" does not exclude other elements or steps, and the words "a" or "an" do not exclude a plurality. A single processor or other unit may fulfill the functions of several items recited in the claims. Although specific elements are recited in dissimilar dependent claims, this does not indicate that combinations of these elements cannot be advantageously used. Computer programs may be stored and / or distributed on suitable media, such as optical storage media or solid-state media provided with or as part of other hardware, but computer programs may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunications systems. No reference numerals in the claims shall be construed as limiting the scope.

Claims

1. A medical system (100, 300, 500), comprising: - A memory (110) storing machine-executable instructions (120) and a magnetic resonance reconstruction module (122), wherein the magnetic resonance reconstruction module is configured to reconstruct a motion-corrected tracer kinetic map (126) based on measured k-space data (124), wherein the measured k-space data is undersampled, wherein the measured k-space data is T1-weighted, and wherein the measured k-space data is dynamic contrast-enhanced k-space data; - A processor (104) configured to control the medical system, wherein the execution of machine-executable instructions causes the processor to: - Receive the k-space data measured by (200); and - The motion-corrected tracer kinetic map is reconstructed (202) by inputting the measured k-space data into the magnetic resonance reconstruction module, wherein the magnetic resonance reconstruction module (122) is configured to reconstruct the motion-corrected tracer kinetic map as a direct model-based reconstruction based on the measured k-space data (124).

2. The medical system according to claim 1, wherein, The magnetic resonance reconstruction module is configured to solve the motion-corrected tracer kinetics map as an optimization problem, wherein the optimization problem includes a motion-compensated regularization term.

3. The medical system according to claim 2, wherein, The regularization term is formulated based on a deformed graph of the motion-corrected tracer kinetics, wherein the deformed graph is time- and space-dependent.

4. The medical system according to claim 3, wherein, The regularization term is also formulated as any one of the following: - Depends on the energy storage function of the deformation diagram; - Depends on the hyperelastic material model of the deformation diagram; - Depends on the curvature-based regularization term of the deformed graph; - A free-form deformation model using a cubic B-spline model that depends on the deformation diagram; and - Depends on the affine transformation model of the deformed graph.

5. The medical system according to any one of claims 2 to 4, wherein, The motion compensation regularization term is a non-rigid body motion compensation regularization term.

6. The medical system according to any one of claims 2 to 4, wherein, The motion compensation regularization term is a rigid body motion compensation regularization term.

7. The medical system according to any one of claims 2 to 6, wherein, The optimization problem is formulated as minimizing the norm of the difference between the measured k-space data and the k-space model, which is configured to map the motion-corrected tracer kinetics plot to the undersampled k-space data, plus the motion-compensation regularization term.

8. The medical system according to any one of claims 2 to 7, wherein, The optimization problem includes: Where r is the spatial location, t is the time, TK(r) is a term of the tracer kinetics graph, R(M(r,t)) is the motion compensation regularization term, d(k,t) is the measured k-space data, M(r,t) is the deformation graph, f(TK(r),M(r,t)) is the forward model for k-space data given TK(r) and M(r,t), and the norm is the mathematical norm.

9. The medical system according to claim 1, wherein, The magnetic resonance reconstruction module is configured to solve the motion-corrected tracer kinetics map as an optimization problem, which is formulated as minimizing the norm of the difference between the measured k-space data and the k-space model, which is configured to map the motion-corrected tracer kinetics map to the undersampled k-space data.

10. The medical system according to claim 9, wherein, The optimization problem includes: Where r is the spatial location, t is the time, TK(r) is a term of the tracer kinetic diagram, d(k,t) is the measured k-space data, M(r,t) is the deformable diagram, f(TK(r),M(r,t)) is the forward model for k-space data given TK(r) and M(r,t), and the norm is the mathematical norm.

11. The medical system according to any one of claims 2 to 10, wherein, The optimization problem is a single optimization problem of directly solving the motion-corrected tracer kinetic map based on the measured k-space data.

12. The medical system according to claim 1, wherein, The magnetic resonance reconstruction module is a neural network, wherein the neural network is trained to output the motion-corrected tracer kinetic map in response to input k-space data, wherein the neural network is trained using any of the following: a motion-corrected tracer kinetic map paired with simulated motion-damaged k-space data; an unsupervised deep learning method to jointly solve for weighting factors and reconstructed training set parameter maps; and combinations thereof.

13. The medical system according to claim 12, wherein, The neural network is any of the following: convolutional neural network, deep neural network, recurrent neural network, a pair of generative adversarial neural networks, a pair of recurrent generative adversarial neural networks, Bayesian neural network, and ADMM-Net.

14. The medical system according to any one of the preceding claims, wherein, The magnetic resonance reconstruction module is configured to solve the motion-corrected tracer kinetics map as an optimization problem or a trained convolutional neural network.

15. The medical system according to any one of the preceding claims, wherein, The tracer kinetics map is a mapping of any of the following: relative extracellular volume, intravascular plasma volume, plasma flow rate, permeability-surface area product, extracellular space outside tissues and blood vessels, inflow mass transfer rate of contrast agent, myocardial blood flow, and combinations thereof.

16. The medical system according to any one of the preceding claims, wherein, The measured k-space data are either first-pass perfusion cardiac k-space data or abdominal dynamic contrast-enhanced k-space data.

17. The medical system according to any one of the preceding claims, wherein, The measured k-space data is undersampled by a factor of at least 5; the measured k-space data is undersampled by a factor of at least 10; the measured k-space data is undersampled by a factor greater than 20; the measured k-space data is undersampled by a factor of at least 30; the measured k-space data is undersampled by a factor of at least 40; the measured k-space data is undersampled by a factor of at least 50; the measured k-space data is undersampled by a factor of at least 60; or the measured k-space data is undersampled by a factor of at least 70. The measured k-space data is undersampled with a factor of at least 80.

18. The medical system according to any one of the preceding claims, wherein, The medical system further includes a magnetic resonance imaging system (502) configured to acquire the measured k-space data from an imaging region. The memory also contains pulse sequence commands (530) configured to acquire the measured k-space data according to a first-pass perfusion cardiac magnetic resonance imaging protocol or an abdominal dynamic contrast-enhanced magnetic resonance imaging protocol. The execution of the machine-executable instructions further enables the processor to control the magnetic resonance imaging system to acquire the measured k-space data using the pulse sequence commands.

19. The medical system according to claim 18, wherein, The pulse sequence command is configured to acquire k-space data using a self-navigating k-space sampling mode.

20. A method for operating a medical system (100, 300, 500), wherein, The method includes: - Receive (200) measured k-space data (124); and - A motion-corrected tracer kinetic map (126) is reconstructed (202) by inputting the measured k-space data into a magnetic resonance reconstruction module (122), wherein the magnetic resonance reconstruction module is configured to reconstruct the motion-corrected tracer kinetic map (126) based on measured k-space data (124), wherein the measured k-space data is undersampled, wherein the measured k-space data is T1-weighted, wherein the measured k-space data is dynamic contrast-enhanced k-space data, wherein the magnetic resonance reconstruction module (122) is configured to reconstruct the motion-corrected tracer kinetic map as a direct model-based reconstruction based on the measured k-space data (124).

21. A computer program product comprising machine-executable instructions for execution by a processor (104) controlling a medical system (100, 300, 500), wherein, The machine-executable instructions include a magnetic resonance reconstruction module (122) configured to reconstruct a motion-corrected tracer kinetic map (126) based on measured k-space data (124), wherein the magnetic resonance reconstruction module (122) is configured to reconstruct the motion-corrected tracer kinetic map as a direct model-based reconstruction based on the measured k-space data (124), wherein the measured k-space data is undersampled, wherein the measured k-space data is T1-weighted, wherein the measured k-space data is dynamically contrast-enhanced k-space data, wherein the execution of the machine-executable instructions causes the processor to: - Receive the k-space data measured by (200); and - The motion-corrected tracer kinetic map is reconstructed (202) by inputting the measured k-space data into the magnetic resonance reconstruction module.

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