Acceleration of multidimensional magnetic resonance imaging (MRI) acquisition via k-space partial sampling and partial reconstruction

Abstract

In some instances, a method for reconstruction of multi-dimensional magnetic resonance imaging (MD-MRI) from partial data is provided. The method comprises acquiring partially-sampled MD-MRI data for a subject, wherein the partially-sampled MD-MRI data indicates spatial frequencies in a k-space; re-organizing, based on a plurality of b-values associated with the partially-sampled MD-MRI data, the partially-sampled MD-MRI data to obtain a plurality of data blocks, wherein each of the plurality of data blocks is associated with a different b-value from the plurality of b-values; reconstructing the partially-sampled MD-MRI data to generate reconstructed MD-MRI data by iteratively reconstructing each data block, from the plurality of data blocks, sequentially based on the b-value associated with the data block; and outputting a magnetic resonance (MR) image based on the reconstructed MD-MRI data.

Description

Leydig 772973 1 ACCELERATION OF MULTIDIMENSIONAL MAGNETIC RESONANCE IMAGING (MRI) ACQUISITION VIA K-SPACE PARTIAL SAMPLING AND PARTIAL RECONSTRUCTION CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Application No.63 / 635,694, filed April 18, 2024, which is herein incorporated by reference in its entirety. STATEMENT OF GOVERNMENT SUPPORT

[0002] This invention was made with Government support under project number ZIA AG000437 by the National Institutes of Health, National Institute on Aging. The United States Government has certain rights in the invention. BACKGROUND

[0003] Diffusion magnetic resonance imaging (MRI) has been widely used in neurological diagnosis to investigate biological information at an intravoxel level (a voxel being a 3D representation of a discrete portion of the imaged biological target). To simultaneously assess the microenvironment characteristic, such as microstructure and local chemical composition, multidimensional MRI (MD-MRI) simultaneously captures diffusion and relaxation data, which may be processed through a model-free estimation of quantitative metrics’ distributions. This information has proven invaluable for studying tissue microstructure, brain connectivity, and pathology. When utilizing diffusion acquisition methods with free gradient waveforms, it becomes possible to explore both frequency-dependent and tensor-related characteristics within the encoding spectrum.

[0004] Nonetheless, MD-MRI demands extended scan times because of the need for multiple acquisitions with variations in both diffusion and relaxation encoding parameters. While there has been progress in the development of an efficient and sparse 40-minute MD- MRI acquisition, providing whole-bran coverage with 2 millimeter cubed (mmଷ^ voxels via 2- dimensional (2D) multi-slice single-shot echo-planar imaging (EPI), this 40-minute protocol remains out of reach for real-world clinical applications. Accordingly, the methods and systems disclosed herein address the limitations described above.Leydig 772973 2 SUMMARY

[0005] In an exemplary embodiment, the present application provides a method for reconstruction of multi-dimensional magnetic resonance imaging (MD-MRI) from partial data, comprising: acquiring partially-sampled MD-MRI data for a subject, wherein the partially- sampled MD-MRI data indicates spatial frequencies in a k-space; re-organizing, based on a plurality of b-values associated with the partially-sampled MD-MRI data, the partially-sampled MD-MRI data to obtain a plurality of data blocks, wherein each of the plurality of data blocks is associated with a different b-value from the plurality of b-values; reconstructing the partially- sampled MD-MRI data to generate reconstructed MD-MRI data by iteratively reconstructing each data block, from the plurality of data blocks, sequentially based on the b-value associated with the data block; and outputting a magnetic resonance (MR) image based on the reconstructed MD-MRI data.

[0006] In some instances, acquiring the partially-sampled MD-MRI data is based on varying a plurality of imaging parameters, wherein the plurality of imaging parameters comprises the plurality of b-values, a plurality of repetition times (TR), and a plurality of echo times (TE).

[0007] In some examples, acquiring the partially-sampled MD-MRI data comprises: acquiring partially-sampled raw MD-MRI data for the subject using a magnetic resonance imaging (MRI) system; and wherein re-organizing the partially-sampled MD-MRI data to obtain the plurality of data blocks comprises re-organizing the partially-sampled raw MD-MRI data to obtain the plurality of data blocks.

[0008] In some variations, the partially-sampled MD-MRI data comprises a plurality of partially-sampled k-space data, wherein each of the plurality of partially-sampled k-space data is associated with a b-value from the plurality of b-values, and wherein re-organizing the partially-sampled MD-MRI data comprises: sorting each of the plurality of partially-sampled k-space data into the plurality of data blocks based on the b-value associated with the partially- sampled k-space data; and organizing the plurality of data blocks into ascending order based on the b-values associated with the plurality of data blocks.

[0009] In some instances, reconstructing the partially-sampled MD-MRI data to generate the reconstructed MD-MRI data comprises: using a first algorithm to reconstruct a first data block, from the plurality of data blocks, wherein the first data block is associated with a first b-value; and using an MD-MRI reconstruction framework to reconstruct a second data block,Leydig 772973 3 from the plurality of data blocks, wherein the first data block is associated with a second b- value that is greater than the first b-value.

[0010] In some examples, using the MD-MRI reconstruction framework to reconstruct the second data block comprises: obtaining a first training block based on the reconstructed first data block; obtaining an initial input for the second data block based on a set of partially- sampled k-space data associated with the second b-value; obtaining an input block for the second data block based on concatenating the first training block and the initial input for the second data block; and using the input block and the MD-MRI reconstruction framework to reconstruct the second data block.

[0011] In some variations, using the input block and the MD-MRI reconstruction framework to reconstruct the second data block comprises: reconstructing the second data block based on using an arguments of the minima (arg min) function and the input block.

[0012] In some instances, reconstructing the second data block is further based on a sensitivity encoding operator, wherein the sensitivity encoding operator is based on a linear operation of a sampling mask, a Fourier operator, and coil sensitivity.

[0013] In some examples, reconstructing the second data block is further based on a block- adaptive regularization parameter that is based on the b-value associated with the second data block.

[0014] In some variations, reconstructing the partially-sampled MD-MRI data to generate the reconstructed MD-MRI data further comprises: using the MD-MRI reconstruction framework to reconstruct one or more additional data blocks, from the plurality of data blocks, wherein the one or more additional data blocks is associated with a third b-value that is greater than the first b-value and the second b-value.

[0015] In some instances, using the MD-MRI reconstruction framework to reconstruct the one or more additional data blocks comprises: obtaining a second training block based on the reconstructed second data block; obtaining an initial input for a third data block based on a second set of partially-sampled k-space data associated with third b-value; obtaining an input block for the third data block based on concatenating the second training block and the initial input for the third data block; and using the input block for the third data block and the MD- MRI reconstruction framework to reconstruct the third data block.

[0016] In another exemplary embodiment, the present application provides a control system for reconstruction of multi-dimensional magnetic resonance imaging (MD-MRI) from partial data, comprising: one or more processors; and a non-transitory computer-readable medium having processor-executable instructions stored thereon, wherein the processor-Leydig 772973 4 executable instructions, when executed by the one or more processors, facilitate: acquiring partially-sampled MD-MRI data for a subject, wherein the partially-sampled MD-MRI data indicates spatial frequencies in a k-space; re-organizing, based on a plurality of b-values associated with the partially-sampled MD-MRI data, the partially-sampled MD-MRI data to obtain a plurality of data blocks, wherein each of the plurality of data blocks is associated with a different b-value from the plurality of b-values; reconstructing the partially-sampled MD- MRI data to generate reconstructed MD-MRI data by iteratively reconstructing each data block, from the plurality of data blocks, sequentially based on the b-value associated with the data block; and outputting a magnetic resonance (MR) image based on the reconstructed MD-MRI data.

[0017] In some instances, acquiring the partially-sampled MD-MRI data is based on varying a plurality of imaging parameters, wherein the plurality of imaging parameters comprises the plurality of b-values, a plurality of repetition times (TR), and a plurality of echo times (TE).

[0018] In some examples, the partially-sampled MD-MRI data comprises a plurality of partially-sampled k-space data, wherein each of the plurality of partially-sampled k-space data is associated with a b-value from the plurality of b-values, and wherein re-organizing the partially-sampled MD-MRI data comprises: sorting each of the plurality of partially-sampled k-space data into the plurality of data blocks based on the b-value associated with the partially- sampled k-space data; and organizing the plurality of data blocks into ascending order based on the b-values associated with the plurality of data blocks.

[0019] In some variations, reconstructing the partially-sampled MD-MRI data to generate the reconstructed MD-MRI data comprises: using a first algorithm to reconstruct a first data block, from the plurality of data blocks, wherein the first data block is associated with a first b-value; and using an MD-MRI reconstruction framework to reconstruct a second data block, from the plurality of data blocks, wherein the first data block is associated with a second b- value that is greater than the first b-value.

[0020] In some instances, using the MD-MRI reconstruction framework to reconstruct the second data block comprises: obtaining a first training block based on the reconstructed first data block; obtaining an initial input for the second data block based on a set of partially- sampled k-space data associated with the second b-value; obtaining an input block for the second data block based on concatenating the first training block and the initial input for the second data block; and using the input block and the MD-MRI reconstruction framework to reconstruct the second data block.Leydig 772973 5

[0021] In some examples, using the input block and the MD-MRI reconstruction framework to reconstruct the second data block comprises: reconstructing the second data block based on using an arguments of the minima (arg min) function and the input block.

[0022] In some variations, reconstructing the second data block is further based on a sensitivity encoding operator, wherein the sensitivity encoding operator is based on a linear operation of a sampling mask, a Fourier operator, and coil sensitivity.

[0023] In some instances, reconstructing the second data block is further based on a block- adaptive regularization parameter that is based on the b-value associated with the second data block.

[0024] In yet another exemplary embodiment, the present application provides a non- transitory computer-readable medium for reconstruction of multi-dimensional magnetic resonance imaging (MD-MRI) from partial data, the non-transitory computer-readable medium having processor-executable instructions stored thereon, wherein the processor-executable instructions, when executed, facilitate: acquiring partially-sampled MD-MRI data for a subject, wherein the partially-sampled MD-MRI data indicates spatial frequencies in a k-space; re- organizing, based on a plurality of b-values associated with the partially-sampled MD-MRI data, the partially-sampled MD-MRI data to obtain a plurality of data blocks, wherein each of the plurality of data blocks is associated with a different b-value from the plurality of b-values; reconstructing the partially-sampled MD-MRI data to generate reconstructed MD-MRI data by iteratively reconstructing each data block, from the plurality of data blocks, sequentially based on the b-value associated with the data block; and outputting a magnetic resonance (MR) image based on the reconstructed MD-MRI data.

[0025] All examples and features mentioned above may be combined in any technically possible way. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The present application will be described in even greater detail below based on the exemplary figures. The application is not limited to the examples described below. All features described and / or illustrated herein can be used alone or combined in different combinations in examples of the application. The features and advantages of various examples of the present application will become apparent by reading the following detailed description with reference to the attached drawings which illustrate the following:Leydig 772973 6

[0027] FIG. 1 shows an exemplary magnetic resonance imaging (MRI) system and / or apparatus in accordance with one or more examples of the present application.

[0028] FIG. 2 shows a representative computing and control environment in accordance with one or more examples of the present application.

[0029] FIG. 3 shows an exemplary process for acquisition and reconstruction of multidimensional (MD)-MRI from incomplete measurements in accordance with one or more examples of the present application.

[0030] FIGs. 4A-4C show example representations of the k-space, sampling mask, and incoherent sampling pattern in accordance with one or more examples of the present application.

[0031] FIGs. 5A and 5B show a flow of data acquisition for MD-MRI in accordance with one or more examples of the present application.

[0032] FIG. 6 shows a flow of data reconstruction in MD-MRI in accordance with one or more examples of the present application.

[0033] FIGs. 7A and 7B show a comparison of MD-MRI images and corresponding error maps in accordance with one or more examples of the present application.

[0034] FIGs. 8A-8C show a comparison of MD-MRI raw images reconstructed using different methods as well as corresponding normalized root mean square error (NRMSE) and structural similarity index (SSIM) graphical representations.

[0035] FIG. 9 shows comparisons of estimated voxelwise signal intensity and voxelwise mean of diffusion and relaxation parameters.

[0036] FIG. 10 shows qualitative comparisons of bin-resolved fractions and their corresponding mean of diffusion and relaxation parameters. DETAILED DESCRIPTION

[0037] Examples of the presented application will now be described more fully hereinafter with reference to the accompanying exemplary figures, in which some, but not all, examples of the application are shown. Indeed, the application may be embodied in any different forms and should not be construed as limited to the examples set forth herein; rather, these examples are provided so that the disclosure will satisfy applicable legal requirements. Where possible, any terms expressed in the singular form herein are meant to also include the plural form and vice versa, unless explicitly stated otherwise. Also, as used herein, the term “a” and / or “an” shall mean “one or more” even though the phrase “one or more” is also used herein.Leydig 772973 7 Furthermore, when it is said herein that something is “based on” something else, it may be based on one or more other things as well. In other words, unless expressly indicated otherwise, as used herein “based on” means “based at least in part on” or “based at least partially on”.

[0038] Systems, methods, and computer program products are herein disclosed that improve acquisition and reconstruction of multidimensional magnetic resonance imaging (MD-MRI) from incomplete measurements. MD-MRI provides valuable subvoxel information. However, currently, it suffers from prohibitively long acquisition time, which makes it impractical for routine clinical use. As such, systems and / or methods are described herein that reduce MD-MRI scan time via partial k-space sampling in conjunction with a new reconstruction framework. For instance, by using the systems and / or methods described below, data reduction is achieved by using random incoherent sampling, followed by locally low-rank reconstruction with block adaptive regularization, and comparison with ground-truth. The results of the systems and / or methods described below have demonstrated in vivo performanceof MD-MRI image reconstruction method that achieves a ^^ ൌ 4 reduction factor. The systemsand / or methods described below have significant potential for clinical neurological applications. MD-MRI is crucial for investigating tissue microstructure, brain connectivity, and pathology in clinical study. Here, the systems and / or methods described below present anovel image reconstruction framework that advantageously allows ^^ ൌ 4 k-space datareduction factor.

[0039] In some examples, the systems and / or methods described herein introduce an innovative MD-MRI reconstruction framework aimed at shortening scan times. This framework leverages incoherent random sampling along spatial and acquisition redundancies, resulting in clinically feasible scan times while maintaining image quality. Missing signals were then reconstructed by solving a constrained optimization problem that combined locally low rank priors with block adaptive regularization. This may demonstrate the feasibility of MD-MRI in addressing real clinical scan time issue. Afterwards, the systems and / or methods described herein were tested based on performing in vivo acquisitions with five adult participants to validate the effectiveness of the method described herein over the conventional method.

[0040] FIG. 1 shows an exemplary magnetic resonance imaging (MRI) system and / or apparatus in accordance with one or more examples of the present application. The system and / or apparatus 1000 includes a controller / interface 1002 that may be configured to apply selected magnetic fields, such as constant or pulsed field gradients, to a subject 1030 or other specimen. An axial magnet controller 1004 is in communication with an axial magnet 1006Leydig 772973 8 that is generally configured to produce a substantially constant magnetic field B0. A gradient controller 1008 is configured to apply a constant or time-varying magnetic field gradient in one or more selected directions or in a set of directions using magnet coils 1010-1012 to produce respective magnetic field gradient vector components Gx, Gy, Gzor combinations thereof to produce the gradients G1, G2, G3 that are associated with b-matrices and / or tensors. A radiofrequency (RF) generator 1014 is configured to deliver one or more RF pulses to a specimen using a transmitter coil 1015. An RF receiver 1016 is in communication with a receiver coil 1018 and is configured to detect or measure net magnetization of spins. Typically, the RF receiver includes an amplifier 1016A and an analog-to-digital convertor 1016B that detect and digitized received signals to obtain the signals S(B). Slice selection gradients may be applied with the same hardware used to apply the diffusion gradients. The gradient controller 1008 may be configured to produce pulses or other gradient fields along one or more axes as needed for a particular b-matrix. By selection of such gradients and other applied pulses, signals associated with a plurality of b-matrices are acquired.

[0041] For imaging, specimens are divided into volume elements (voxels) and MR signals for a plurality of gradient directions are acquired as discussed above, but signals may be acquired for one or only a few specimen voxels. In typical examples, signals are obtained for some or all voxels of interest.

[0042] A computer 1024 or other processing system such as a personal computer, a workstation, a personal digital assistant, laptop computer, smart phone, server, computing platform, computing system, and / or a networked computer may be provided for acquisition, control, and / or analysis of specimen data. The computer 1024 generally includes a hard disk, a removable storage medium such as a floppy disk or compact disc read-only memory (CD- ROM), and / or other memory such as random access memory (RAM). Data may also be transmitted to and from a network using cloud-based processors and storage. Data may be uploaded to the Cloud or stored elsewhere. Computer-executable instructions for, e.g., data acquisition or control, b-matrix computations, such as random selected of directions and random selected of b-magnitudes as well as determining the associated b-matrices, and tensors and distribution estimations may be provided on a floppy disk or other storage medium such as a memory or delivered to the computer 1024 via a local area network, the Internet, or other network. Signal acquisition, instrument control, and signal analysis may be performed locally or with distributed processing. For example, signal acquisition and signal analysis may be performed at different locations. Signal evaluation may be performed remotely from signal acquisition by communicating stored data to a remote processor. In general, control and dataLeydig 772973 9 acquisition with the MRI system and / or apparatus may be provided with a local processor, or via instruction and data transmission via a network.

[0043] FIG. 2 shows a representative computing and control environment in accordance with one or more examples of the present application. FIG.2 and the following discussion are intended to provide a brief, general description of an exemplary computing / data acquisition environment in which the disclosed technology may be implemented. Although not required, the disclosed technology is described in the general context of computer executable instructions, such as program modules, being executed by a personal computer (PC), a mobile computing device, tablet computer, servers, computing platforms, and / or other computational and / or control device, system, and / or apparatus. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform particular tasks or implement particular abstract data types. Moreover, the disclosed technology may be implemented with other computer system configurations, including, multiprocessor systems, network PCs, minicomputers, mainframe computers, and the like. The disclosed technology may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote memory storage devices.

[0044] With reference to FIG. 2, an exemplary system for implementing the disclosed technology includes a general purpose computing device in the form of an exemplary conventional PC 1100, including one or more processing units 1102, a system memory 1104, and a system bus 1106 that couples various system components including the system memory 1104 to the one or more processing units 1102. The system bus 1106 may be any of several types of bus structures including a memory bus or memory controller, a peripheral bus, and a local bus using any of a variety of bus architectures. The exemplary system memory 1104 includes read only memory (ROM) 1108 and random access memory (RAM) 1110. A basic input / output system (BIOS) 1112, including the basic routines that help with the transfer of information between elements within the PC 1100, is stored in ROM 1108.

[0045] The exemplary PC 1100 further includes one or more storage devices 1110 (e.g., non-transitory computer-readable mediums) such as a hard disk drive for reading from and writing to a hard disk, a magnetic disk drive for reading from or writing to a removable magnetic disk, an optical disk drive for reading from or writing to a removable optical disk (such as a CD-ROM or other optical media), and a solid state drive. Such storage devices may be connected to the system bus 1106 by a hard disk drive interface, a magnetic disk driveLeydig 772973 10 interface, an optical drive interface, or a solid state drive interface, respectively. The drives and their associated computer readable media provide nonvolatile storage of computer- readable instructions, data structures, program modules, and other data for the PC 1100. Other types of computer-readable media which may store data that is accessible by a PC, such as magnetic cassettes, flash memory cards, digital video disks, compact discs (CDs), digital video discs (DVDs), RAMs, ROMs, and the like, may also be used in the exemplary operating environment.

[0046] A number of program modules may be stored in the storage devices 1110 including an operating system, one or more application programs, other program modules, and program data. A user may enter commands and information into the PC 1100 through one or more input devices 1140 such as a keyboard and a pointing device such as a mouse. Other input devices may include a digital camera, microphone, joystick, game pad, satellite dish, scanner, or the like. These and other input devices are often connected to the one or more processing units 1102 through a serial port interface that is coupled to the system bus 1106, but may be connected by other interfaces such as a parallel port, game port, or universal serial bus (USB). A monitor 1146 or other type of display device is also connected to the system bus 1106 via an interface, such as a video adapter. Other peripheral output devices, such as speakers and printers may be included. Additionally, and / or alternatively, one or more further output devices 1145 may be also connected to the system bus 1106. The output devices 1145 may include one or more additional monitors, other visual output devices such as display devices, audio output devices, and / or other devices that communicate and / or provide information to the user.

[0047] The PC 1100 may operate in a networked environment using logical connections to one or more remote computers, such as a remote computer 1160. In some examples, one or more network or communication connections 1150 are included. The remote computer 1160 may be another PC, a server, a router, a network PC, or a peer device or other common network node, and typically includes many or all of the elements described above relative to the PC 1100, although only a memory storage device 1161 has been illustrated in FIG.2. The personal computer 1100 and / or the remote computer 1160 can be connected to a logical a local area network (LAN) and a wide area network (WAN). Such networking environments are commonplace in offices, enterprise wide computer networks, intranets, and the Internet.

[0048] When used in a LAN networking environment, the PC 1100 is connected to the LAN through a network interface. When used in a WAN networking environment, the PC 1100 typically includes a modem or other means for establishing communications over the WAN, such as the Internet. In a networked environment, program modules depicted relative to theLeydig 772973 11 personal computer 1100, or portions thereof, may be stored in the remote memory storage device or other locations on the LAN or WAN. The network connections shown are exemplary, and other means of establishing a communications link between the computers may be used.

[0049] The memory 1104 generally includes computer-executable instructions for performing one or more operations, functions, algorithms, and / or processes described herein. For example, memory portion 1162 may store computer-executable instructions for determining gradient directions, and computer-executable instructions for b-matrix computation and random b-magnitude and direction selection may be stored at 1173B or previously computed b-matrix specification can be stored in memory portion 1173A. Computer-executable instructions for processing acquired signals (for example, determining mean diffusion tensor and covariance) may be stored in a memory portions 1160, 1171. Computer-executable instructions for data acquisition and control are stored in a memory portion 1170. Acquired and processed data may be displayed using computer-executable instructions stored at memory portion 1171. As noted above, data acquisition, processing, and instrument control may be provided at an MRI system 1174 such as the MRI system described in FIG.1 above, or distributed at one or more processing devices using a LAN or WAN.

[0050] FIG. 3 shows an exemplary process for acquisition and reconstruction of multidimensional (MD)-MRI from incomplete measurements in accordance with one or more examples of the present application. The process 1200 may be performed by a control system such as the computer 1024 from FIG.1, the PC 1100 from FIG.2, and / or other control systems (e.g., mobile computing devices, tablet computers, servers, computing platforms, or other computational and / or control devices, systems, and / or apparatuses). However, it will be recognized that any of the following blocks may be performed in any suitable order, the blocks may be performed by any suitable system, and that the process 1200 may be performed in any suitable environment. The descriptions, illustrations, and processes of FIG. 3 are merely exemplary and the process 1200 may use other descriptions, illustrations, and processes.

[0051] At block 1202, the control system acquires partially-sampled MD-MRI data for a subject, and the partially-sampled MD-MRI data indicates spatial frequencies in a k-space. The partially-sampled MD-MRI data may be acquired using an incoherent sampling mask and / or other schemes or methods. The k-space is an abstract concept and may refer to a data matrix that includes raw MD-MRI data. The k-space is an array of numbers (e.g., values and / or measurements) representing spatial frequencies in the magnetic resonance (MR) image, and when subjected to mathematical function or formula such as a transform (e.g., an inverse Fourier transform), it generates a final MR image. The cells (e.g., entries) of k-space areLeydig 772973 12 typically arranged on a rectangular grid with principal axes kx and ky, corresponding to the horizontal (x-) and vertical (y-) axes of the image. Unlike the image domain, where positions are represented, the k-space axes represent spatial frequencies in the x- and y-directions. While individual points (kx, ky) in k-space do not directly correspond to individual pixels (x, y) in the image, each k-space point includes spatial frequency and phase information about every pixel in the final image. Conversely, each pixel in the image corresponds to every point in k-space. This relationship between image and k-space is reminiscent of the diffraction patterns seen in x-ray crystallography, optics, and / or holography.

[0052] The control system may use MD-MRI to acquire the MD-MRI data (e.g., the partially-sampled MD-MRI data) for the subject. In the methods and processes described herein, the k-space MD-MRI data is directly subsampled using an incoherent sampling scheme. For instance, diffusion MRI is commonly employed in neurological diagnosis for probing intravoxel biological information. MD-MRI extends these capabilities by simultaneously capturing diffusion and relaxation data, which may be analyzed using a model-free approach to obtain distributions of valuable quantitative metrics. To simultaneously encode both diffusion and relaxation, it requires multiple combinations of imaging parameters (e.g., repetition time (TR), echo time (TE), and b-value) along the acquisition domain. The parameters establish image domain properties of the output image, e.g., varying them would result in changes to the output image contrast.

[0053] The TR may be the amount of time between successive pulse sequences applied to the same slice. The TE may be the time between the delivery of the RF pulse and the receipt of the echo signal. The b-value may be a degree or factor that reflects the strength and timing of the gradients used to generate the diffusion-weighted images. Therefore, in MD-MRI, the control system may obtain the raw MD-MRI data based on varying the imaging parameters (e.g., TR, TE, and / or the b-value) along the acquisition domain. This will be described in FIGs. 4A-4C.

[0054] For instance, FIGs.4A-4C show example representations 1302-1306 of the k-space, sampling mask, and incoherent sampling pattern in accordance with one or more examples of the present application. The k-space representation 1302 shows a cell of the k-space, which is arranged on a rectangular grid with principle axes kx and ky. The sampling mask representation 1304 shows a sampling mask. The representation 1306 shows the incoherent sampling pattern in the k-m space with a reduction factor of 4. For instance, the x-axis of the representation 1306 is the acquisition domain (m) and the y-axis of the representation 1306 is the k-space. As mentioned previously, the k-space data is in two-dimensions (e.g., kx and ky). But, because theLeydig 772973 13 control system samples via lines (e.g., horizontal lines that are shown in the sampling mask 1304 and are in nature two dimensions), the k-m space shown in representation 1306 is also in two-dimensions.

[0055] In some variations, the control system uses k-space incoherent sampling (e.g., an incoherent sampling scheme) to take advantages of data redundancy. This subsampling strategy may be used in dynamic MRI and multi-contrast imaging. The k-space MD-MRI data is directly subsampled using an incoherent sampling scheme (e.g., representations 1304 and 1306 in FIGs. 4B and 4C). Each k-space subsampled MD-MRI volume is acquired with a unique set of imaging parameters, e.g., varying repetition time (TR), echo time (TE), and b- tensor. Varying the imaging parameters and repeating the acquisition constitutes the MD-MRI dataset (e.g., the raw MRI data). The existence of multiple sets of imaging parameters creates multiple images with varying contrasts of the same object (e.g., brain), which implies that data redundancy in the image / k-space domains may be exploited by using incoherent sampling in both local and global domain.

[0056] Referring back to block 1202, the control system may use an MRI device, system, and / or apparatus (e.g., the entire system and / or apparatus 1000 and / or portions of the system and / or apparatus 1000) to obtain the MD-MRI data indicating a partially sampled k-space (e.g., the partially sampled MD-MRI data). For instance, the control system may use an MD-MRI technique such as by varying imaging parameters including the TR, TE, and / or b-tensor. Afterwards, the control system may obtain the MD-MRI data (e.g., the raw MD-MRI data) that indicates the spatial frequencies using an incoherent random sampling mask, and thus acquire a partial k-space. For example, the MD-MRI data may be a two-dimensional data matrix and each entry (e.g., cell) indicates a spatial frequency and is associated with a coordinate (e.g., a kx coordinate and a ky coordinate). The MD-MRI data is directly acquired using the sampling pattern described above, resulting in partial k-space MD-MRI raw data, which may then be used in blocks 1204-1208 below.

[0057] For example, using one or more k-space sampling patterns, the control system acquires the raw MD-MRI data to generate and / or obtain the partially-sampled MD-MRI data (e.g., a plurality of partially-sampled k-space data). Each of the partially-sampled MD-MRI data (e.g., each of the plurality of partially-sampled k-space data) may be associated with a unique set of imaging parameters (e.g., TR, TE, and / or b-tensor). The partially-sampled MD- MRI data may include entries, but based on the k-space incoherent sampling, certain entries may be missing (e.g., set to a value of 0 or omitted). For instance, based on applying the sampling masks (e.g., the sampling mask from representation 1304), certain entries from theLeydig 772973 14 partially-sampled MD-MRI data may be missing. The control system may perform partial sampling of the raw MD-MRI k-space data to reduce the amount of data that is needed for image reconstruction, thus enabling the acceleration of the acquisition.

[0058] The partially-sampled MD-MRI data may be used in reconstruction to generate the final MRI image, which is described below.

[0059] In general, to perform image reconstruction from partially-sampled k-space, missing k-space signal may be interpolated using low rank (LR) approaches.

[0060] In conventional diffusion MRI (e.g., regular diffusion MRI that does not involve MD-MRI), LR is generally used to interpolate the missing k-space signal with combining data fidelity. The assumption is that brain structural information along the acquisition domain (e.g., the diffusion weighting experimental parameter, b, here denoted with index m) remains similar with smoothness of coil sensitivity. Under this assumption, missing signals in k-m space may then be reconstructed by solving a constrained optimization problem that minimizes spatial and acquisition domain with respect to the data fidelity constraint.

[0061] Compared with general diffusion MRI, MD-MRI requires multiple sets of imaging parameters to encode both diffusion and relaxation. In addition to diffusion encoding parameter b, relaxation parameters such as TR and TE are varying along the acquisition domain. This implies that the acquisition domain cannot be described by a single imaging parameter such as the b-value or number of directions, and therefore the index m describes a given set of TE, TR, and b parameters combination. This implicates that regularization to interpolate the missing signal in the MD-MRI k-m space is performed on the local domain by using local regularization parameter. Given these considerations, process 1200 provides a novel reconstruction framework that employs locally LR priors with block adaptive regularization to suppress the noise while maintaining the contrast information.

[0062] At block 1204, the control system re-organizes the partially sampled MD-MRI data (e.g., the plurality of partially-sampled k-space data) based on the b-values. For example, once the partially-sampled k-space data (e.g., the partially-sampled MD-MRI data) is acquired and prior to image reconstruction, the control system reorganizes the data according to b-values of each acquisition index, to allow differentiation of penalties along the local domains. Groups of the same b-value, which are defined as a block, are sorted by ascending b-value order. Blocks are then column vectorized and horizontally concatenated to construct a matrix. This is described and shown in FIGs.5A and 5B.

[0063] FIGs.5A and 5B show a flow 1350 of data acquisition for MD-MRI in accordance with one or more examples of the present application. For example, the flow 1350 includes aLeydig 772973 15 data acquisition step 1352, which is shown in FIG.5A, and a reorganization step 154, which is shown in FIG. 5B. Initially, referring to FIG. 5A, the control system performs the data acquisition step 1352. For example, as mentioned previously, the control system may obtain the partially-sampled MD-MRI data. The partially-sampled MD-MRI data may be associated with different imaging parameters. For instance, as shown in FIG. 4C, the graphical representation 1306 shows the k-m space with the y-axis being the k-space and the x-axis being the acquisition domain (m space). Here, in FIG.5A, the control system acquires the partially- sampled MD-MRI data that are in the k-m space, and further obtains (e.g., determines, retrieves, and / or receives) imaging parameters associated with the m-space. For instance, for m=1 (e.g., the first partially-sampled k-space data within the partially-sampled MD-MRI data), the associated imaging parameters may be a b-value of 0, a TR of 5700 milliseconds (ms), and a TE of 47 ms. For m=2, the associated imaging parameters may be a b-value of 1500 s / mm2, a TR of 5700 ms, and a TE of 73 ms. As such, the control system obtains partially-sampled MD-MRI data comprising multiple different partially-sampled k-space data that are oriented along the acquisition domain (m-space), and each number of m (e.g., m=1 or m=2) along the acquisition domain has associated imaging parameters such as TE, TR, and b-values.

[0064] Referring to FIG.5B, at step 1354 (e.g., the reorganization step), the control system performs block 1204 and re-organizes the partially-sampled MD-MRI data into a plurality of blocks (e.g., data blocks), and each block is associated with a particular b-value. For instance, after data acquisition, the control system obtains the partially-sampled MD-MRI data that are arranged along the acquisition domain (m-space). Then, based on an imaging parameter (e.g., the b-value), the control system re-organizes the partially-sampled k-space data into a plurality of blocks. For example, as shown, the first block (e.g., B0) includes a set of partially-sampled k-space data that have the b-value of 0, the second block (e.g., B1) includes a second set of partially-sampled k-space data that have a b-value of 1000 s / mm2, and so on. As such, the control system may include the partially-sampled k-space data associated with m=1 into the first block (e.g., B0), the partially-sampled k-space data associated with m=2 into the third block (e.g., B2), the partially-sampled k-space data associated with m=3 into the second block (e.g., B1), and so on.

[0065] In other words, at block 1204, the control system obtains (e.g., generates, sorts, and / or determines) a plurality of data blocks for the partially-sampled MD-MRI data. The partially-sampled MD-MRI data includes partially-sampled k-space data, and each partially- sampled k-space data is associated with a particular m value in the m space. Each of the data blocks has an associated b-value (e.g., b-value of 0, 1000 s / mm2, and so on), and the controlLeydig 772973 16 system sorts the partially-sampled k-space data into each of the data blocks based on the b- values that are associated with the partially-sampled k-space data. For example, for the first block (e.g., block B0) associated with a b-value of 0, the control system determines which of the partially-sampled k-space data has an associated b-value of 0, and groups the partially- sampled k-space data together into the first block. The control system then moves on to the second block, the third block, and so on.

[0066] To put it another way, in some variations, the control system sorts each of the plurality of partially-sampled k-space data into the plurality of data blocks based on the b-value associated with the partially-sampled k-space data. Afterwards, the control system organizes the plurality of data blocks into ascending order based on the b-values associated with the plurality of data blocks. As such, after performing block 1204, the MD-MRI data is re- organized into data blocks in ascending order based on the b-value. For instance, the first data block has a lowest b-value (e.g., b-value of 0), the second data block has a second lowest b- value (e.g., b-value of 1000 s / mm2), the third data block has a third lowest b-value (e.g., b- value of 1500 s / mm2), and so on.

[0067] In some instances, block 1204 is optional. For example, at block 1202, the control system may acquire the partially-sampled MD-MRI data such that they are already in the proper order (e.g., in the ascending b-value order). For instance, at a first step, the control system may use the MD-MRI system to acquire the partially-sampled k-space data for the first block (e.g., B0) associated with a first b-value (e.g. b-value=0). At a second step, the control system may acquire the partially-sampled k-space data for the second block (e.g., B1) associated with a second b-value that is greater than the first b-value (e.g., b-value=1000 s / mm2), and so on. Given that the partially-sampled MD-MRI data is already in the proper order, the control system might not perform 1204.

[0068] At block 1206, the control system reconstructs the partially-sampled MD-MRI data to generate reconstructed MD-MRI data using an iterative solver (e.g., the MD-MRI reconstruction framework described below). For example, the control system may reconstruct the MD-MRI data to generate reconstructed MD-MRI data by iteratively reconstructing each data block, from the plurality of data blocks, sequentially based on the b-value associated with the data block (e.g., based on ascending b-value). The control system may perform block 1206 using methods such as block adaptive regularization and reconstruction of MD-MRI data from incomplete measurements.

[0069] Referring to block adaptive regularization, the first block (b=0 or B0) is used as a reference volume, and for that reason, the control system acquires this block using conventionalLeydig 772973 17 regular k-space sampling (e.g., generalized auto-calibrating partially parallel acquisitions (GRAPPA) and / or sensitivity encoding (SENSE)). Therefore, the control system acquires the first block (b=0) at low acceleration factor (2~3) with large number of Nyquist sample region in the data acquisition step to cover the coil sensitivity and preserve image quality. The reconstructed block, which is defined as trained block (XT), is then augmented into the next block. The input block (XG) is then constructed by concatenation of XT and the block to be reconstructed (XB): XG = [XT, XB]

[0070] Total size of the trained block XT is extended after XB is reconstructed. Each reconstruction step (e.g., the reconstruction boxes shown in FIG. 6 such as the boxes 1402, 1404, and 1406) is performed with different penalties (λୋ^in Eq.1) based on the b-value: the lower the b-value, the higher the penalty, and vice-versa.

[0071] Referring to reconstruction of MD-MRI data from incomplete measurements, in the below, a reconstruction framework of MD-MRI is introduced that incorporates the model into the measurement model, while being formulated as a constrained minimization problem with locally low rank prior and block adaptive penalty using the following objective function: arg mଡ଼ృin^ฮYୋ െ E X ฮଶ ^λ ∑ ฮP ^X ^ฮ . Eq. (1)^ଶ^ ୋ^ ୋ^ ଶ ୋ^ ୯∈ஐ ୯ ୋ^ ∗

[0072] to n-th inputblock. Yୋ^(∈ LM × Nb) is the group of acquired k-m space signals corresponding to n-th input block where L is the number of coil elements, M is the number of measured encodings (k-spacenumber in each m-index), and Nb is the number of n-th input block size (e.g., Yୋభ = ^Y^బ , Y^భ ൧,Yୋమ = ^Yୋభ , Y^మ ൧ … Yୋొ = ^Yୋొషభ , Y^ొ ൧). Eୋ^is the sensitivity encoding operator of the n-thinput block. Eୋ^is a linear operation of sampling mask, Fourier operator, and coil sensitivity, such that Eୋ^=Mୋ^FSୋ^, where Mୋ^is the multiplication of sampling mask of the n-th input block, F is the Fourier operator, and Sୋ^is the coil sensitivity of the n-th input block. Coil sensitivity maps are estimated using the fully acquired k-space data from the Nyquist region B0 block (i.e., b=0 block). Xୋ^is the target artifact free MD-MRI images of the n-th input block, λୋ^is block-adaptive regularization parameter that depends on the b-value of the n-th input block, P is an operator that extracts and reshapes one local spatial patch at pixel-index, q as a vector in G୬. Hyper parameter λୋ^is empirically controlled by several values based on the normalized root-mean-square deviation error and iteration number. Ω is the set of all non- overlapping covering patches that uniformly tile in the image domain (e.g., a set of patchesLeydig 772973 18 extracting at the voxel position in Xୋ^, considering the patch size (m x n)). The control system then reconstructs every block from B1to BNsequentially using Eq. 1 above with different penalties. To differentiate penalties on each block reconstruction, the control system controls λୋ^using the exponential function: λୋ^ ൌ ^^ ∗ ^^^^^^ି^^∗^^ , ^^ ൌ 1 … ..^^ (block number) Eq. ^2^

[0073] In to specify the shape of the exponential function. Here,0.005 and 0.8, respectively. However, the control system may set “a” and “b” to other values in other examples. Hence, in the resulting final reconstructed blocks (e.g., images), high-b value blocks are, if compared with low b-value blocks, much less weighted. Iteration number is empirically chosen based on the convergence speed and rate. Block 1206, the block adaptive regularization, and the reconstruction of MD- MRI data from incomplete measurements will be described in further detail below using FIG. 6.

[0074] FIG. 6 shows a flow 1400 of data reconstruction in MD-MRI in accordance with one or more examples of the present application. At block 1206, the control system may perform flow 1400 to reconstruct the MD-MRI data (e.g., the partially-sampled MD-MRI data that have been re-organized into data blocks based on b-values) to generate reconstructed MD- MRI imaging data using an iterative solver.

[0075] For instance, initially, for the first block (e.g., B0) that is associated with a first b- value (e.g., a b-value of 0), the control system might not use the MD-MRI reconstruction framework described above (e.g., Eq. 1), and may instead use a first algorithm (e.g., a conventional algorithms such as GRAPPA and / or SENSE). This is shown in box 1402. For example, based on using the conventional algorithms (e.g., reconstruction), the control system obtains a trained block for B0.

[0076] In other words, as mentioned above, after re-organization, the control system obtains the partially-sampled MD-MRI data that are sorted into different data blocks associated with different b-values. As such, the first data block (B0) initially includes fully-sampled k- space data that has a first b-value (e.g., b-value of 0). Using a conventional algorithm, the control system reconstructs the fully-sampled k-space data from the first data block (B0) to obtain reconstructed imaging data for the first data block. Thus, after using the conventional algorithm on the set of fully-sampled k-space data associated with the first b-value, the control system generates a trained block (e.g., trained data block) for the first data block (B0) that includes the reconstructed imaging data.Leydig 772973 19

[0077] After obtaining the reconstructed first block (e.g., the trained data block for B0), the control system may iteratively use the previous trained block and an initial input (e.g., the zero- padded image of the set of partially-sampled k-space data) to obtain an input block. Subsequently, the control system may use the MD-MRI reconstruction framework to convert the input block into a trained block for the associated b-value.

[0078] For example, referring to box 1404, the control system uses the trained data block for B0 (e.g., the reconstructed k-space data for the first data block) and the initial input to generate the input block, and then uses reconstruction to obtain the trained block. As mentioned above, the trained data block B0 is the reconstructed k-space data for the first b- value. In addition, the initial input is a zero-padded image of the set of partially-sampled k- space data for the second data block (e.g., B1) that is associated with a second b-value. For example, the control system may obtain the zero-padded image for the second data block (e.g., the second data block associated with a second b-value) based on using a transformation (e.g., an inverse Fourier transform) on the set of partially-sampled k-space data associated with the second b-value. In other words, the control system performs a transformation (e.g., inverse Fourier transform) to transform or convert the set of partially-sampled k-space data for the second data block (e.g., associated with a second b-value of 1000 s / mm2) into a zero-padded image for the second data block.

[0079] Afterwards, the control system uses the initial input (e.g., the zero-padded image for the second data block) and the trained block (e.g., the reconstructed set of imaging data for the first data block) to obtain or generate the input block for the second data block. To obtain or generate the input block, the control system may concatenate the trained block and the initial input. Therefore, the control system generates the input block (XG) using the trained block (XT) and the initial input (XB). For instance, in FIG. 6, for box 1404, the input block is ^^ீ^భ , the initial input is ^^^^భ , and the trained block is ^^ బ்.

[0080] Thesystem then uses the input block to determine the reconstructed block and the trained block for the second data block (e.g., B1), which is associated with a second b- value (e.g., b-value of 1000 s / mm2). For example, using the MD-MRI reconstruction framework described above (e.g., Eq. 1), the control system may determine the second reconstructed block / the trained block based on the input block. For instance, the control system may use an optimization algorithm (e.g., arguments of the minima (arg min) function) and the input block to determine the trained block associated with the second b-value. TheLeydig 772973 20 trained block associated with the second b-value is the reconstructed imaging data for the set of partially-sampled k-space data associated with the second b-value.

[0081] For instance, as mentioned above, the set of partially-sampled k-space data includes missing or omitted entries due to a sampling mask. The control system obtains the input block and applies Eq. 1 to fill in the missing entries. For instance, the control system obtains the input block based on concatenating the initial input (e.g., the set of partially-sampled k-space data with the missing entries that is transformed using an inverse Fourier transform) and the trained block for the previous data block). Thus, the input block also includes missing entries due to the set of partially-sampled k-space data. Using the MD-MRI reconstruction framework, the control system populates the missing entries based on Eq. 1. For instance, the control system generates input points for the missing entries of the input block and determines when the MD-MRI reconstruction framework (e.g., Eq. 1) is minimized. The control system populates the missing entries of the input block using the input points that minimize the MD- MRI reconstruction framework. Thus, in some examples, using the MD-MRI reconstruction framework, the control system generates the reconstructed block and the trained block for the second data block B1 (e.g., the data block associated with the second b-value of 1000 s / mm2) based on populating the input block with the determined input points (e.g., the input points that minimize Eq. 1). As mentioned above, the MD-MRI reconstruction framework is described above using Eq.1 and Eq.2. In some instances, the MD-MRI reconstruction framework might not include all of the parameters, variables, and / or components from Eq. 1 and Eq. 2. Additionally, and / or alternatively, the control system may modify certain parameters, variables, and / or components from Eq. 1 and Eq. 2 (e.g., the scalar parameters “a” and “b” from Eq.2) prior to using the MD-MRI reconstruction framework.

[0082] The control system may iteratively determine the trained blocks for the next data block based on using the trained block from the previous data blocks until a final trained block is determined. For example, in box 1406, the control system determines a trained block for the third data block (B2) associated with a third b-value (e.g., b-value of 1500 s / mm2) using the trained block for the second data block (B1). For instance, the control system obtaining the trained block for the second data block (B1) is described above. The control system may further determine the initial input for the third data block (e.g., the zero-padded image) based on transforming the set of partially-sampled k-space data for the third data block using a transformation (e.g., an inverse Fourier transform). The control system may use the initial input for the third data block and the trained block for the second data block to obtain an input block for the third data block (e.g., based on concatenating the initial input and the trainedLeydig 772973 21 block for the second data block). The control system may then use the initial input for the third data block and the MD-MRI reconstruction framework to obtain the reconstructed block / the trained block for the third data block. The control system may then iteratively repeat the above process until the reconstructed block for the last data block (e.g., the data block BNassociated with the b-value of 3000 s / mm2) is obtained. This is shown in box 1408 (e.g., use the initial input and the trained block to obtain an input block, and then use reconstruction to obtain an output).

[0083] Therefore, each data block builds off of the previous determinations of the previous data block until the final reconstructed block for the last data block is determined. For instance, after reconstructing the first data block (B0), the control system obtains the first trained block. In FIG.6, the reconstructed first data block may be ^^^^^^^^^^^^ீబ ൌ ^^^బ, and thus the trained first data block would be based on ^^^^^^^^బand may be ^^ బ்ൌ ^^^బ with ^^^బ being the same as^^^^^^^^బ. Then, for the second data block (B1) associated with the second b-value (e.g., b-value of , the control system uses the first trained block (^^ బ்ൌ ^^^బ) and the initial input(^^^^భ ൌ ^^^^^௧) to determine the input block (^^ ^ீ^భൌ ^^^బ்,^^^భ^). The control system uses the MD-MRI reconstruction framework and the input block to determine the reconstructed block for the second data block (B1), which may be ^^^^^^^ீభ ൌ ^^^బ்,^^^^^^^^భ^. Using the reconstructed block, the control system obtains the^).

[0084] Afterwards, using the trained block for the second data block (B1) and the initial input (^^^^మ ൌ ^^^^^௧) for the third data block (B2) that is associated with a third b-value, thecontrol system determines the input block for the third data block, and the input block may be ^^^ீమ ൌ ^^^^భ்,^^^మ^. As such, from the third data block onwards, the trained block that is used to the input block does not include solely information from the previous block (e.g., B1), but also information from the other previous blocks as well (e.g., also includes information associated with B0). The additional information is used to determine the input blocks that are then fed into the MD-MRI reconstruction framework. Thus, using the MD-MRI reconstruction framework, the control system obtains the reconstructed block for the third data block, which would be ^^^^^^^ ൌ ^^^,^^^^^^^^, an^^^^^ீమభ்^మd the trained block, which would be ^^ మ் ൌ ^^^ భ்,^^^మ^. The control system continues for the other data blocks. For the final data block (BN), the control system obtains the input block ^^ீ^ ^ಿ ൌ ^^^ேି^,^^^ಿ^ based on the previous trained block and theLeydig 772973 22 initial input (^^^ ൌ ^^ ), and the reconstructed block for th^^^^^^ಿ ^^^௧ e final data block ^^ீಿൌ ^^^^^^^^ேି^,^^^ಿ^. words, conventional reconstruction algorithms (e.g., SENSE or GRAPPA)solvers to estimate the final solution while the above method is using an iterative solver. Thus, the above method includes sub-index ^^ in Xୋ୩ ୩^ = [X^^, X^^]. ^^ denotes the iteration number of each block and n denotes the input block number. For the first block reconstruction, first block X^బis directly reconstructed by using the conventional method. Then, X^బwhich is the final reconstructed image from the B0 block is defined as the trained block (X ^ ^^బ). To reconstruct the second block (B1), the initial input is Xୋభ= [X^భ, X^భ= X୧୬୧^] and the final solution of second block (final reconstructed image, XB) is X ^୧୬ୟ୪ ୋ^୧୬ୟ୪భ = [X^భ, X^భ= X^]. X୧୬୧^is the zero-padded image, which is obtained via an inverse Fourier transform on each block k-space data. The final solution X^is then augmented into the previous X^^షభand defined as new X^^before performing the next block reconstruction (See FIG.6). Every block is sequentially reconstructed by using Eq. 1 with alternating direction method of multipliers (ADMM).

[0086] At block 1208, the control system outputs an MR image based on the reconstructed MD-MRI data. For instance, based on the reconstructed data block(s), the control system outputs the MD-MRI imaging data obtained from the partially-sampled k-space. The control system may output the MR image on a display device such as the monitor 1146 shown in FIG. 2.

[0087] The following describes test results using the above MD-MRI reconstruction framework. For instance, the data acquisition is described.

[0088] Five healthy participants were each scanned on a 3 T whole body MR scanner using 2-dimensional (2D) multi-slice single shot echo-planar imaging (EPI) with embedded free- gradient waveforms. Experimental procedures were performed in compliance with local Institutional Review Board, and participants provided written informed consent. The acquisition parameters were set as follows: field of view (FOV^ ൌ 228 ൈ 228 ൈ 110 mmଷ,voxel size ൌ 2 ൈ 2 ൈ 2 mmଷ , acquisition bandwidth = 1512 hertz / pixel (Hz / Px), in-planeacceleration factor 2 using GRAPPA reconstruction with 24 reference lines, effective echo spacing of 0.8 millisecond (ms), phase-partial Fourier factor of 0.75, and axial slice orientation. Numerically optimized linear, planar, and spherical b-tensors were employed with b-values ranging between 0.1 and 3 ms / micrometer square (µm2) in the range of 6.6 െ 21 Hz centroidLeydig 772973 23frequencies ^ω / 2π^ , and with different combinations of repetition times, TR ൌ^0.62, 1.75, 3.5, 5, 7, 7.6^ s and echo times, TE ൌ ^40, 63, 83, 150^ ms, comprising a total of139 volumes and 40 minutes acquisition time.

[0089] The study was conducted retrospectively, in which full k-space data is first acquired and reconstructed using conventional GRAPPA (defined as the Reference images), and then Fourier transformed to produce fully-sampled k-space data. These fully-sampled MD-MRI data sets are retrospectively sub-sampled using the random incoherent sampling mask shown in block 1306 along both spatial and acquisition domains while retaining the same spatial resolution as the Reference (See FIGs.7A and 7B described below). The reduced data sets are reconstructed using the above method and compared to two other methods: global low rank (LR), which uses a single image as a patch for each acquisition index, and conventional SENSE. It should be noted, however, that in practice, reduced-sampled k-space data need only be acquired. The fully-sampled k-space data was acquired here for comparison purposes.

[0090] After MD-MRI k-space data is reconstructed into imaging data, the estimation of diffusion and relaxation parameters are descried below. Imaging data was processed using the Monte Carlo inversion algorithm as implemented in the multidimensional diffusion MRItoolbox. Briefly, the ^^^^^^ െ ^^^^ െ ^^^^ encoded signal S is modeled as a sum ofcontributions; the ith component is characterized by its signal weight, or fraction ^^^, tensor- valued diffusion spectra ^^^^^^^, and longitudinal and transverse relaxation rates R^,୧and Rଶ,୧according to ^ ^^^b^w^, TE, TR^ ൌ ^^^^ exp^െ^ ^^^^^^:^^^^^^^^^^^ ^ ^1 െ exp൫െ^^^^^^^,^൯൧exp൫െ^^^^^^ଶ,^൯

[0091] The results are described below. The reconstructed data volumes are first explained. FIGs.7A and 7B show the reconstructed MD-MRI images and corresponding error maps by using the above method with varying reduction factors, R=3.5 to 4.5. For instance, FIGs.7A and 7B show a comparison of MD-MRI images and corresponding error maps in theabove method with varying R ൌ 3.5 to 4.5. Note that with increasing reduction factor, R ൌ 4shows the better suppression of noise and aliasing artifact than R ൌ 4.5 along both spatial andacquisition direction (green arrows).

[0092] Compared with R=4.5, R=4 image shows better suppression of noise and aliasing artifact in both spatial and acquisition domains. Furthermore, R=4 image shows the nearly identical image quality as compared to R=3.5. FIGs.8A-8C show the reconstructed MD-MRILeydig 772973 24 images using different methods as well as corresponding normalized root mean square error (NRMSE) values and structural similarity index (SSIM) values using R=4. For instance, FIG. 8A shows the comparison of the reference image and MD-MRI raw images reconstructed using the proposed method, global Low-rank (LR), and conventional SENSE. Specifically, the first row shows the images based on B = 200 s / mm2, the error map (e.g., the NRMSE), and the SSIM. Note that the above method shows better suppression of noise and clear delineation of structure compared with global low-rank and conventional SENSE (enlarged box). Furthermore, the above method substantially estimates better than comparison methods in both NRMSE and SSIM, along the acquisition domain as compared to the reference (see the graphical representations shown in FIGs. 8B and 8C). In addition, it is noted that the above method shows lowest reconstruction error while maintaining the highest SSIM along the acquisition domain.

[0093] Moving to processed MD-MRI parametric maps, the performance of the above method is examined and its effect on estimated voxelwise signal intensity (^^^), mean isotropic diffusivity ^^^^^^^^^^^, mean squared normalized anisotropy ^^^^^^2^^, mean longitudinal and ∆ transverse relaxation rates ^^^^^^^^, and ^^^^^ଶ^, respectively). FIG.9 shows these maps obtained using the different reconstruction approaches with R=4, compared to the Reference. For instance, FIG.9 shows the estimated voxelwise signal intensity, the mean isotropic diffusivity, the mean squared normalized anisotropy, and the mean longitudinal and transverse relaxation rates for the reference, the Proposed R = 4, the Global LR and SENSE. The above method shows reliable delineation of fine structural details and suppression of noise as compared to global LR and SENSE. For instance, FIG.9 shows a comparison of ^^^and voxelwise mean of diffusion and relaxation parameters with the proposed method, Global Low-rank, and Conventional SENSE at reduction factor R=4. The above method yields better suppression of artifacts and noise than global low-rank and conventional SENSE (as shown by the arrows). Note that the above method shows clearly delineated and very close to the Reference, while those compared methods are contaminated by artifact and noise (enlarged box).

[0094] The means in FIG. 9 may be computed over sub-divisions (“bins”) of the distribution space, typically comprising three bins in the in vivo human brain, roughly corresponding to white matter (WM), gray matter (GM), and cerebrospinal fluid (CSF). In FIG. 10, signal fractions are compared. In addition, WM bin-resolved mean diffusion, relaxation, and directionally encoded color (DEC) maps under a reduction factor of R=4, utilizing various reconstruction methods and the Reference maps for comparison are shown. For instance, FIG.Leydig 772973 25 10 shows a qualitative comparison of bin-resolved fractions and their corresponding mean of diffusion and relaxation parameters using the proposed method, global Low-rank, and conventional SENSE. Note that fine structures are more conspicuously delineated compared with those in compared methods (enlarged box). It is noted that the above method yields better suppression of noise and shows clear structural delineation.

[0095] Therefore, the above introduces a MD-MRI image reconstruction method that achieves R=4 reduction factor in k-space data, and successfully demonstrated its performance in vivo using Reference data in a retrospective study design. This framework provides whole- brain, 2 mmଷvoxels, MD-MRI, while maintaining robustness and accuracy of the processed maps. This work is expected to expend its clinical feasibility and application to various neurological disease.

[0096] Each reference in the following list of references is hereby incorporated by reference herein in its entirety:

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[0115] It will be appreciated that the figures of the present application and their corresponding descriptions are merely exemplary, and that the application is not limited to these exemplary situations.Leydig 772973 27

[0116] It will further be appreciated by those of skill in the art that the execution of the various machine-implemented processes and steps described herein may occur via the computerized execution of processor-executable instructions stored on a non-transitory computer-readable medium, e.g., random access memory (RAM), read-only memory (ROM), programmable read-only memory (PROM), volatile, nonvolatile, or other electronic memory mechanism. Thus, for example, the operations described herein as being performed by computing devices and / or components thereof may be carried out by according to processor- executable instructions and / or installed applications corresponding to software, firmware, and / or computer hardware.

[0117] The use of the term “at least one” followed by a list of one or more items (for example, “at least one of A and B”) is to be construed to mean one item selected from the listed items (A or B) or any combination of two or more of the listed items (A and B), unless otherwise indicated herein or clearly contradicted by context. The terms “comprising,” “having,” “including,” and “containing” are to be construed as open-ended terms (i.e., meaning “including, but not limited to,”) unless otherwise noted. Recitation of ranges of values herein are merely intended to serve as a shorthand method of referring individually to each separate value falling within the range, unless otherwise indicated herein, and each separate value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g., “such as”) provided herein, is intended merely to better illuminate the application and does not pose a limitation on the scope of the application unless otherwise claimed. No language in the specification should be construed as indicating any non-claimed element as essential to the practice of the application.

[0118] It will be appreciated that the examples of the application described herein are merely exemplary. Variations of these examples may become apparent to those of ordinary skill in the art upon reading the foregoing description. The inventors expect skilled artisans to employ such variations as appropriate, and the inventors intend for the application to be practiced otherwise than as specifically described herein. Accordingly, this application includes all modifications and equivalents of the subject matter recited in the claims appended hereto as permitted by applicable law. Moreover, any combination of the above-described elements in all possible variations thereof is encompassed by the application unless otherwise indicated herein or otherwise clearly contradicted by context.

Claims

Leydig 772973 28 CLAIMS:

1. A method for reconstruction of multi-dimensional magnetic resonance imaging (MD- MRI) from partial data, the method comprising: acquiring partially-sampled MD-MRI data for a subject, wherein the partially-sampled MD-MRI data indicates spatial frequencies in a k-space; re-organizing, based on a plurality of b-values associated with the partially-sampled MD-MRI data, the partially-sampled MD-MRI data to obtain a plurality of data blocks, wherein each of the plurality of data blocks is associated with a different b-value from the plurality of b-values; reconstructing the partially-sampled MD-MRI data to generate reconstructed MD-MRI data by iteratively reconstructing each data block, from the plurality of data blocks, sequentially based on the b-value associated with the data block; and outputting a magnetic resonance (MR) image based on the reconstructed MD-MRI data.

2. The method of claim 1, wherein acquiring the partially-sampled MD-MRI data is based on varying a plurality of imaging parameters, wherein the plurality of imaging parameters comprises the plurality of b-values, a plurality of repetition times (TR), and a plurality of echo times (TE).

3. The method of claim 1, wherein acquiring the partially-sampled MD-MRI data comprises: acquiring partially-sampled raw MD-MRI data for the subject using a magnetic resonance imaging (MRI) system; and wherein re-organizing the partially-sampled MD-MRI data to obtain the plurality of data blocks comprises re-organizing the partially-sampled raw MD-MRI data to obtain the plurality of data blocks.

4. The method of claim 1, wherein the partially-sampled MD-MRI data comprises a plurality of partially-sampled k-space data, wherein each of the plurality of partially-sampled k-space data is associated with a b-value from the plurality of b-values, and wherein re- organizing the partially-sampled MD-MRI data comprises: sorting each of the plurality of partially-sampled k-space data into the plurality of data blocks based on the b-value associated with the partially-sampled k-space data; andLeydig 772973 29 organizing the plurality of data blocks into ascending order based on the b-values associated with the plurality of data blocks.

5. The method of claim 1, wherein reconstructing the partially-sampled MD-MRI data to generate the reconstructed MD-MRI data comprises: using a first algorithm to reconstruct a first data block, from the plurality of data blocks, wherein the first data block is associated with a first b-value; and using an MD-MRI reconstruction framework to reconstruct a second data block, from the plurality of data blocks, wherein the first data block is associated with a second b-value that is greater than the first b-value.

6. The method of claim 5, wherein using the MD-MRI reconstruction framework to reconstruct the second data block comprises: obtaining a first training block based on the reconstructed first data block; obtaining an initial input for the second data block based on a set of partially-sampled k-space data associated with the second b-value; obtaining an input block for the second data block based on concatenating the first training block and the initial input for the second data block; and using the input block and the MD-MRI reconstruction framework to reconstruct the second data block.

7. The method of claim 6, wherein using the input block and the MD-MRI reconstruction framework to reconstruct the second data block comprises: reconstructing the second data block based on using an arguments of the minima (arg min) function and the input block.

8. The method of claim 7, wherein reconstructing the second data block is further based on a sensitivity encoding operator, wherein the sensitivity encoding operator is based on a linear operation of a sampling mask, a Fourier operator, and coil sensitivity.

9. The method of claim 7, wherein reconstructing the second data block is further based on a block-adaptive regularization parameter that is based on the b-value associated with the second data block.Leydig 772973 30 10. The method of 6, wherein reconstructing the partially-sampled MD-MRI data to generate the reconstructed MD-MRI data further comprises: using the MD-MRI reconstruction framework to reconstruct one or more additional data blocks, from the plurality of data blocks, wherein the one or more additional data blocks is associated with a third b-value that is greater than the first b-value and the second b-value.

11. The method of claim 10, wherein using the MD-MRI reconstruction framework to reconstruct the one or more additional data blocks comprises: obtaining a second training block based on the reconstructed second data block; obtaining an initial input for a third data block based on a second set of partially- sampled k-space data associated with third b-value; obtaining an input block for the third data block based on concatenating the second training block and the initial input for the third data block; and using the input block for the third data block and the MD-MRI reconstruction framework to reconstruct the third data block.

12. A control system for reconstruction of multi-dimensional magnetic resonance imaging (MD-MRI) from partial data, comprising: one or more processors; and a non-transitory computer-readable medium having processor-executable instructions stored thereon, wherein the processor-executable instructions, when executed by the one or more processors, facilitate: acquiring partially-sampled MD-MRI data for a subject, wherein the partially- sampled MD-MRI data indicates spatial frequencies in a k-space; re-organizing, based on a plurality of b-values associated with the partially- sampled MD-MRI data, the partially-sampled MD-MRI data to obtain a plurality of data blocks, wherein each of the plurality of data blocks is associated with a different b-value from the plurality of b-values; reconstructing the partially-sampled MD-MRI data to generate reconstructed MD-MRI data by iteratively reconstructing each data block, from the plurality of data blocks, sequentially based on the b-value associated with the data block; and outputting a magnetic resonance (MR) image based on the reconstructed MD- MRI data.Leydig 772973 31 13. The control system of claim 12, wherein acquiring the partially-sampled MD-MRI data is based on varying a plurality of imaging parameters, wherein the plurality of imaging parameters comprises the plurality of b-values, a plurality of repetition times (TR), and a plurality of echo times (TE).

14. The control system of claim 12, wherein the partially-sampled MD-MRI data comprises a plurality of partially-sampled k-space data, wherein each of the plurality of partially-sampled k-space data is associated with a b-value from the plurality of b-values, and wherein re- organizing the partially-sampled MD-MRI data comprises: sorting each of the plurality of partially-sampled k-space data into the plurality of data blocks based on the b-value associated with the partially-sampled k-space data; and organizing the plurality of data blocks into ascending order based on the b-values associated with the plurality of data blocks.

15. The control system of claim 12, wherein reconstructing the partially-sampled MD-MRI data to generate the reconstructed MD-MRI data comprises: using a first algorithm to reconstruct a first data block, from the plurality of data blocks, wherein the first data block is associated with a first b-value; and using an MD-MRI reconstruction framework to reconstruct a second data block, from the plurality of data blocks, wherein the first data block is associated with a second b-value that is greater than the first b-value.

16. The control system of claim 15, wherein using the MD-MRI reconstruction framework to reconstruct the second data block comprises: obtaining a first training block based on the reconstructed first data block; obtaining an initial input for the second data block based on a set of partially-sampled k-space data associated with the second b-value; obtaining an input block for the second data block based on concatenating the first training block and the initial input for the second data block; and using the input block and the MD-MRI reconstruction framework to reconstruct the second data block.

17. The control system of claim 16, wherein using the input block and the MD-MRI reconstruction framework to reconstruct the second data block comprises:Leydig 772973 32 reconstructing the second data block based on using an arguments of the minima (arg min) function and the input block.

18. The control system of claim 17, wherein reconstructing the second data block is further based on a sensitivity encoding operator, wherein the sensitivity encoding operator is based on a linear operation of a sampling mask, a Fourier operator, and coil sensitivity.

19. The control system of claim 17, wherein reconstructing the second data block is further based on a block-adaptive regularization parameter that is based on the b-value associated with the second data block.

20. A non-transitory computer-readable medium for reconstruction of multi-dimensional magnetic resonance imaging (MD-MRI) from partial data, the non-transitory computer- readable medium having processor-executable instructions stored thereon, wherein the processor-executable instructions, when executed, facilitate: acquiring partially-sampled MD-MRI data for a subject, wherein the partially-sampled MD-MRI data indicates spatial frequencies in a k-space; re-organizing, based on a plurality of b-values associated with the partially-sampled MD-MRI data, the partially-sampled MD-MRI data to obtain a plurality of data blocks, wherein each of the plurality of data blocks is associated with a different b-value from the plurality of b-values; reconstructing the partially-sampled MD-MRI data to generate reconstructed MD-MRI data by iteratively reconstructing each data block, from the plurality of data blocks, sequentially based on the b-value associated with the data block; and outputting a magnetic resonance (MR) image based on the reconstructed MD-MRI data

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