Abstract:
One aspect of the present disclosure provides an imaging method including: specifying an imaging focus region on a subject to be imaged, applying radiofrequency pulses to the subject to interact with a magnetic field gradient, wherein the radiofrequency pulses successively bend magnetization phases of respective electromagnetic signals from the specified imaging focus region, resulting in magnified pixel data, and generating a magnified image of the imaging focus region based on the magnified pixel data.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims the benefit of and priority to U.S. Provisional Application 62/059,520 filed Oct. 3, 2014, which is incorporated herein by reference in its entirety. 
     
    
     GOVERNMENT RIGHTS STATEMENT 
       [0002]    The invention described herein was developed with support from the National Institute of Health under contract HHSN263200900028I. The U.S. government may have certain rights to the invention. 
     
    
     TECHNICAL FIELD 
       [0003]    The present subject matter relates generally to magnetic resonance imaging (MRI) systems, algorithms, and methods, and more particularly, to selectively enhancing the resolution of an area during an MRI scan. 
       BACKGROUND 
       [0004]    Magnetic resonance imaging (MRI) is a widely used medical imaging technique used to investigate and diagnose the anatomy and/or physiology of the body. Typical MRI scanners use a combination magnetic fields and radiowaves to form images of the body. In general, MRI is a slow imaging method. This is partly because MRI is based on frequency space (e.g., k-space) line-scanning techniques. As such, it is inherently time-consuming to generate high-dimensional images with high spatial resolution. In most MRI exams, the operator prescribes a “slice” or “slices” in a region of interest (e.g., a kidney, a tumor, and the like) of a subject to be imaged. Because of the intrinsic properties of MRI, the slices have to be scanned line-by-line in k-space with different phase-encoding for each line. 
         [0005]    In order to image the region of interest with a high spatial resolution, existing MRI techniques spend an excessive amount of time imaging the entire slice with equal spatial resolution. In other words, it is necessary to generate a uniform image resolution across the entire image slice. This produces an “all or nothing” approach which wastes scanning time, as the entire slice must be imaged to high spatial resolution so as to attain the desired high spatial resolution at certain region of interest. As a result, spatial resolution is often sacrificed due to practical time constraints on the scanning process, which leads to loss of fine anatomical details. 
         [0006]    MRI data acquisition can be accelerated by partial parallel imaging (PPI) which reduces the number of k-space lines needed to form an image by taking advantage of the inherent localizing power in the heterogeneous sensitivity profiles of multi-channel receiver coils. PPI has improved clinical MRI and found widespread applications by either increasing imaging speed for the same spatial resolution, or equivalently, increasing spatial resolution for the same scan time. However, clinical PPI is limited to low imaging acceleration (i.e., &lt;2×) due to noise amplification and convolution of artifacts at high acceleration rate. Accordingly, there is a need for MRI techniques capable of reducing the scan time necessary to image a subject at an increased focal spatial resolution without the imaging limitations suffered by PPI. If such a technique is compatible with PPI, then the increase in spatial resolution from it and that from PPI can multiply each other. 
       SUMMARY 
       [0007]    According to embodiments of the present disclosure, an imaging method includes: specifying an imaging focus region on a subject to be imaged, applying radiofrequency pulses to the subject to interact with a magnetic field gradient, wherein the radiofrequency pulses successively bend magnetization phases of respective electromagnetic signals from the specified imaging focus region. Phase bending by radiofrequency pulses has the effect of stretching the imaging focus region in a phase-encoding direction, resulting in magnified pixel data, and generating an image of the object with magnified imaging focus region based on the magnified pixel data. 
         [0008]    According to embodiments of the present disclosure, the radiofrequency pulses to be applied can be constructed according to a process that includes: designing a smoothly-varying monotonic magnetization phase curve from −π to π as the phase module, designing a trapezoid magnetization amplitude module with its two top vertices smoothed, extending the phase module at both ends to match the bottom two vertices of the amplitude module, and designing the radiofrequency pulses such that an amplitude of the frequency response of the radiofrequency pulses substantially matches the amplitude module, and a phase of the frequency response of the radiofrequency pulses substantially matches the phase module and its multiples. The radiofrequency pulses may be designed using Fourier transform. 
         [0009]    According to embodiments of the present disclosure, the generating of the magnified image may include: reconstructing the magnified pixel data in order to form the magnified image of the imaging focus region. The magnified pixel data may be reconstructed using Fourier transform. The generating of the magnified image also include: mathematically inverting a process by which the magnified pixel data was formed and/or experimentally measuring a magnetization magnitude and a phase module on an imaging phantom and regridding the magnified pixel data to a larger image size in a phase-encoding direction and/or smoothing the magnified image. 
         [0010]    According to embodiments of the present disclosure, a plurality of imaging focus regions on the subject to be imaged may be specified. Further, the imaging focus region may be specified inside an image field-of-view. Even further, a length of aperture stop may be specified inside the image field-of-view. Yet even further, the region of interest may be a kidney, a tumor, or the like. 
         [0011]    According to embodiments of the present disclosure, a non-transitory computer readable medium containing program instructions executable by a processor includes: program instructions that specify an imaging focus region on a subject to be imaged, program instructions that apply radiofrequency pulses to a region of interest of the subject to interact with a magnetic field gradient, wherein the radiofrequency pulses successively bend magnetization phases of respective electromagnetic signals from the specified imaging focus region, resulting in magnified pixel data, and program instructions that generate a magnified image of the imaging focus region based on the magnified pixel data. 
         [0012]    According to embodiments of the present disclosure, a magnetic resonance imaging device includes: a magnetic field gradient controller programmed to control operation of a magnetic field gradient amplifier to alter a spinning frequency of atomic nuclei within a subject, a radio frequency pulse controller programmed to control operation of a radiofrequency transmitter to apply radiofrequency pulses to a region of interest within the subject, an analog/digital signal converter programmed to convert analog signals received by a radiofrequency receiver coil, and an imaging sequence controller programmed to: specify an imaging focus region on the subject; apply radiofrequency pulses to the region of interest of the subject to interact with a magnetic field gradient, wherein the radiofrequency pulses successively bend magnetization phases of respective electromagnetic signals from the specified imaging focus region, resulting in magnified pixel data; and generate a magnified image of the imaging focus region based on the magnified pixel data 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0013]    For a fuller understanding of the nature and desired objectives of the present subject matter, reference is made to the following detailed description taken in conjunction with the accompanying drawing figures. Like reference numerals denote corresponding parts throughout the several views. 
           [0014]      FIG. 1  depicts examples of amplitude- and phase-modulated radiofrequency pulses which bend the magnetization phase at a predefined imaging focus according to embodiments of the present disclosure. 
           [0015]      FIG. 2  depicts examples of one-dimensional magnification imaging and reconstruction according to embodiments of the present disclosure. 
           [0016]      FIG. 3  depicts an example of phantom experiments according to embodiments of the present disclosure. 
           [0017]      FIGS. 4A-4C  depict another example of phantom experiments according to embodiments of the present disclosure. 
           [0018]      FIGS. 5A-5D  depict examples of in vivo applications of magnetic resonance magnification imaging according to embodiments of the present disclosure. 
           [0019]      FIGS. 6A-6B  depict additional examples of in vivo applications of magnetic resonance magnification imaging according to embodiments of the present disclosure. 
           [0020]      FIGS. 7A-7E  depict examples of partial parallel magnification imaging according to embodiments of the present disclosure. 
           [0021]      FIG. 8  depicts a schematic diagram of an example MRI system according to embodiments of the present disclosure. 
           [0022]      FIG. 9  depicts examples of phase-bending radiofrequency pulses generated using Eq. [2] and their frequency response. 
           [0023]      FIGS. 10A and 10B  depict examples of magnification imaging of a rat brain. 
           [0024]      FIGS. 11A-11C  depict pixel changes using magnification with linearly varying spatial resolution. 
           [0025]      FIG. 12  shows an example of 4× magnification imaging of a phantom with three teeth. 
           [0026]      FIG. 13  shows an example of multi-foci magnification. 
       
    
    
     DEFINITIONS 
       [0027]    For the purposes of the present application, the following terms will have the following meanings unless specifically stated otherwise: 
         [0028]    The phrase “Magnetic Resonance Imaging” or “MRI” as used herein means the process by which certain nuclei, when placed in a magnetic field, absorb and release energy in the form of radio waves that are analyzed by a computer, thereby producing an image (e.g., of structures, human anatomy, and physiological information). The present subject matter and methods can be employed with MRI generated with MRI equipment from any manufacturer. In some embodiments, the MRI equipment or scanner shall have a scanner housing with a magnet with a typical magnetic field (B 0 ), ranging from about 0.5 to about 7 Tesla or higher, positioned inside the housing. In biomedical applications, the subject to be imaged (e.g., a human body) lies on the scanner table or is disposed within the bore of the MRI equipment and the hydrogen and other nuclei in the subject are realigned in certain directions. Magnetic field gradient coils are arranged near the imaged subject to superimpose on B 0  an additional selected spatially-varying magnetic field. One or more radiofrequency (RF) coils are arranged inside the bore of the magnet to transmit RF excitation and inversion pulses (B 1 ). The RF coils also measure the RF magnetic resonance signal emitted from the imaged subject. The gradient coils and the RF transmitter coils are turned on and off at specific strengths and for specific duration according in a predetermined sequence of actions collectively called an imaging sequence. At specific time points during the execution of the imaging sequence, the RF receiver coils measure the RF signals emitted from the subject. Images of structures such as body parts or organs are created from the measured RF signals during or after the completion of the imaging sequence. 
         [0029]    The term “memory” as used herein encompasses both volatile memory (e.g., random access memory and the like) and non-volatile memory (e.g., read-only memory, hard disks, floppy discs, magnetic tape, optical discs, paper table, punch cards, and the like). 
         [0030]    The term “subject” as used herein shall be understood to include any animal including mammals including, but not limited to, humans, primates, as well as non-living objects. 
         [0031]    The term “slice” as used herein shall be understood to include both two-dimensional and three-dimensional images of an object. 
         [0032]    As used in the specification and claims, the singular form “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise. 
         [0033]    Unless specifically stated or obvious from context, as used herein, the term “about” is understood as within a range of normal tolerance in the art, for example within 2 standard deviations of the mean. “About” can be understood as within 10%, 9%, 8%, 7%, 6%, 5%, 4%, 3%, 2%, 1%, 0.5%, 0.1%, 0.05%, or 0.01% of the stated value. Unless otherwise clear from context, all numerical values provided herein are modified by the term about. 
         [0034]    As used in the specification and claims, the terms “comprises,” “comprising,” “containing,” “having,” and the like can have the meaning ascribed to them in U.S. patent law and can mean “includes,” “including,” and the like. 
         [0035]    Ranges provided herein are understood to be shorthand for all of the values within the range. For example, a range of 1 to 50 is understood to include any number, combination of numbers, or sub-range from the group consisting of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, or 50 (as well as fractions thereof unless the context clearly dictates otherwise). 
         [0036]    Unless specifically stated or obvious from context, as used herein, the term “or” is understood to be inclusive. 
       DETAILED DESCRIPTION 
       [0037]    As noted above, in order to image the region of interest with a high spatial resolution, existing MRI techniques spend an excessive amount of time imaging the entire slice with equal spatial resolution. In other words, it is necessary to generate a uniform image resolution across the entire image slice. This produces an “all or nothing” approach which wastes scanning time, as the entire slice must be imaged with uniform high spatial resolution to attain the desired high spatial resolution at a region of interest. As a result, spatial resolution is often sacrificed due to practical time constraints on the scanning process, which leads to loss of fine anatomical details. Accordingly, there is a need for MRI techniques capable of reducing the scan time necessary to image a subject at an increased focal spatial resolution. 
         [0038]    For the sake of comparison, in optical magnification, travelling electromagnetic rays can be bent by a convex magnifier such that details from the focus of the magnifier fill a disproportionally large area of the field-of-view. Conversely, in conventional MRI, such magnification of a region of interest is not possible. 
         [0039]    Aspects of the present disclosure address the above shortcomings of conventional MRI techniques by selectively enhancing the resolution of an area during an MRI scan. Stated generally, aspects of the present disclosure magnify a region of interest during an MRI scan by using specially designed radiofrequency pulses to interact with magnetic field gradients such that the magnetization phase at the region of interest is bent precisely as prescribed herein. By successively bending the phase of electromagnetic signals from the region of interest, the differential phase evolution at the region of interest is made faster than conventional MRI, leading to focal resolution enhancement in a manner similar to optical magnification, as described above. Because phase encoding is one of the most time-consuming parts of MRI, the techniques described herein (i.e., “magnetic resonance magnification imaging”) reduce scan time for a predefined focal spatial resolution. Or equivalently, the techniques increase spatial resolution at the imaging focus for the same scan time. Notably, the magnetic magnification imaging techniques of the present disclosure may produce up to 4× magnifying power at a single predefined focus region. 
       Theory 
       [0040]    RF Pulses for Bending Magnetization Phase at Region of Interest 
         [0041]    Within the realm of linear response theory the transverse magnetization M xy (r) excited by a RF pulse B 1 (t) (t ε 0˜T p ) is related by Fourier transform: 
         [0000]        M   xy ( r )= iM   0 ∫ 0   T     p     B   1 ( t ) e   −i2πGrt   dt   [1]
 
         [0000]    where G is the magnetic field gradient vector. For an amplitude-modulated RF pulse (i.e., no imaginary components), M xy (r) has a linear phase gradient which can be cancelled by magnetic field gradient reversal. Eq. [1] can be inverted to craft complex RF pulses that bend the magnetization phase at region of interest. Examples of phase-bending complex RF pulses generated by inverting Eq. [1] and their frequency response calculated using Bloch equations are shown in  FIGS. 1 and 9 . 
         [0042]    M xy (r) predicted by Eq. [1] may deviate from Bloch simulation. When necessary, this deviation, ΔM xy (r), can be corrected by noting that when B 1 (t) deviates from the linear response theory ΔB 1 (t) still meet the requirements of the linear response theory since |ΔB 1 (t)|&lt;&lt;|B 1 (t)|. Therefore, the corrected complex RF pulse B 1 (t)′ can be calculated using inverse Fourier transform 
         [0000]        B   1 ( t )′∝∫ −∞   +∞ ( M   xy ( r )+Δ M   xy ( r )) e   i2πGrt   dr   [2]
 
         [0000]    Details on designing RF pulses for bending magnetization phase at imaging focus are provided in further detail below. 
         [0043]    Magnification Encoding and Image Reconstruction 
         [0044]    In conventional MRI, spin density ρ (r) is related to k-space signal s(k) by Fourier transform 
         [0000]        s ( k )=∫ −∞   +∞ ρ( r ) e   −i2πkr   dr   [3]
 
         [0000]    By successively bending the magnetization phase at region of interest using RF pulses described by Eq. [2], ρ(r) is modulated by spatially dependent phase function σ(r) (e.g., see  FIG. 1 ). Accordingly, Eq. [3] is generalized to 
         [0000]        s (σ)=∫ −∞   +∞ ρ( r ) e   −i2πσ(r)   dr   [4]
 
         [0045]    Eq. [4] can be linearized by remapping spin density into a warped space φ=φ (r) such that 
         [0000]      σ( r )=σφ  [5]
 
         [0000]    where the phase encoding step counter σ is independent of r. φ(r) describes magnetization phase (φ(r) ε−0.5˜0.5) produced by the RF pulse for phase encoding step σ=1. Substituting Eq. [5] into Eq. [4] and perform inverse Fourier transform we obtain 
         [0000]    
       
         
           
             
               
                 
                   
                     ρ 
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         [0046]    in Eq. [6] compensates for intensity changes accompanied by stretching the object. The reconstructed ρ(φ(r)) image is then regridded to generate the desired spin density map ρ(r). 
         [0047]    The uniform pixel size Δx 0  in conventional MRI with N points equals to field-of-view (FOV)/N, which is now generalized to the following in magnification imaging: 
         [0000]    
       
         
           
             
               
                 
                   
                     Δ 
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         [0000]    Focal magnification is achieved at imaging focus where 
         [0000]    
       
         
           
             
               FOV 
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             &gt; 
             1. 
           
         
       
     
         [0048]    Phase-Bending RF Pulse Design Based on Linear Response Theory 
         [0049]    Magnification imaging is based on interactions between magnetic field gradients used in conventional MRI and specially designed radiofrequency pulses to successively bend magnetization phase at imaging focus. For illustration purposes, we describe here designing RF pulses that produce an arctangent phase responses. The phase template φ(r) is given by 
         [0000]    
       
         
           
             
               
                 
                   
                     ϕ 
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                       ( 
                       r 
                       ) 
                     
                   
                   = 
                   
                     
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                        
                       
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                           r 
                         
                         ) 
                       
                     
                     
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                   8 
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         [0000]    Here r is normalized by FOV. For 2× magnification at r=0, we have 
         [0000]    
       
         
           
             
               
                 
                   d 
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         [0000]    when α=4.66. The transverse magnetization amplitude has a trapezoid shaped with its two slopes smoothed using half-sine functions. The flat top of the trapezoid matches the image FOV with its phase described by Eqs. [5] and [8]. Then a series of N complex RF pulses were generated using Eq. [2] as in  FIG. 9  for σ 
         [0000]    
       
         
           
             
               ɛ 
               - 
               
                 N 
                 2 
               
               + 
               1 
             
             ∼ 
             
               
                 N 
                 2 
               
               . 
             
           
         
       
     
         [0000]    The RF pulse for σ=0 is a sinc-like pulse with no imaginary components. Each {σ, −σ} pulse pair form a Hermitian function because Eq. [2] is invariant to simultaneous time reversal and complex conjugation. 
         [0050]      FIG. 9  top row shows the complex RF pulse for σ=64 with the arctangent phase profile generated by inverting Eq. [1] and its frequency response for flip angle=45°. Small distortion in magnitude of the excited transverse magnetization is seen at imaging focus. Since the magnetization phase profile remains ideal the magnitude profile was fitted using a fourth order polynomial. ΔM xy (r) was synthesized from fit residuals and σ(r) given by Eq. [8]. ΔB 1 (t)×32 calculated from ΔM xy (r) was shown in the left panel of the bottom row of  FIG. 9 . Results from Bloch simulation of the corrected RF pulse B 1 (t)′ were given in the bottom row. A second iteration was found to be unnecessary. 
         [0051]    Furthermore,  FIGS. 10A and 10B  illustrate example images of a rat brain generated according to various imaging methodologies. In particular,  FIGS. 10A and 10B , on left, each show a horizontal image of rat brain by conventional spin echo MRI with uniform spatial resolution. In contrast,  FIG. 10A , on right, shows a 2× magnified image of the rat brain using 128 pulses with arctangent phase profiles. Similarly,  FIG. 10B , on right, shows a 3× magnified image of the rat brain using 128 pulses with a phase template described by φ(r)=A(atan(αr))+Br, where A=0.276, B=0.243, and α=10.0. 
         [0052]    Magnification with Linearly Varying Spatial Resolution 
         [0053]    Instead of focal magnification, an image with linearly varying spatial resolution can also be very useful for many applications. The phase template Φ(r) is given by 
         [0000]      Φ( r )=0.6 r   2   +r− 0.15  [9]
 
         [0000]    for rε−½˜½. Note that spatial resolution and pixel size here vary linearly across the field of view and 
         [0000]    
       
         
           
             
               
                 
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             ; 
             
               
                 
                   
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                 1 
                  
                 
                   : 
                 
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                 4. 
               
             
           
         
       
     
         [0000]    The imaging results are shown in  FIGS. 11A-11C  where the image pixel size changes linearly along the phase-encoding direction after regridding.  FIG. 11A  shows a regular MRI with uniform spatial resolution across the entire field of view. The field of view is 32 mm and matrix size is 256×128.  FIG. 11B  is the raw image generated using 128 phase bending radiofrequency pulses. In  FIG. 11B , the object seems to be stretched with the degree of stretching varying linearly across the object. In  FIG. 11C , the image was regridded to 2014 in phase encoding direction, with the image pixel size changing linearly along the phase-encoding direction with no smoothing performed. 
       Magnetic Resonance Imaging Devices 
       [0054]    Referring now to  FIG. 8 , an exemplary magnetic resonance imaging (MRI) device  1  is depicted. The MRI device  1  includes a scanner housing with a magnet having a typical magnetic field (B 0 ), ranging from about 0.5 to about 7 Tesla or higher, positioned inside the housing. When the subject to be imaged, for example a human body lying on the scanner table  2 , is disposed within the bore of the MRI equipment, the hydrogen and other nuclei in the subject are realigned in certain directions. Magnetic field gradient coils  3  are arranged near the imaged subject to superimpose on B 0  an additional selected spatially-varying magnetic field. One or more radiofrequency (RF) coils  8  are arranged inside the bore of the magnet to transmit RF excitation and inversion pulses (B 1 ). The RF coils  8  also measure the RF magnetic resonance signal emitted from the imaged subject. (Some RF coils can be used to both transmit and receive RF signals, while other RF coils are used to only transmit or receive signals. The work done in this study utilized the same coil to transmit and receive RF signals. However, concepts discussed here can be applied to any type of coils.) The gradient coils  3  and the RF transmitter coils  8  are turned on and off at specific strengths and for specific duration according in a predetermined sequence of actions collectively called an imaging sequence implemented by an imaging sequence controller  6 . At specific time points during the execution of the imaging sequence, the RF receiver coils  8  measure the RF signals emitted from the body. Images of body parts or organs are created from the measured RF signals during or after the completion of the imaging sequence by the image reconstruction module  11 . 
         [0055]    The MRI device  1  can include one or more modules programmed to control the operation of the MRI device  1 . For example, an image sequence memory module  5  can store one or more imaging sequence algorithms, as described herein, that specify the relative timing on one or more RF and field gradient pulses. The stored imaging sequence algorithms can, for example, control the design of radiofrequency pulses that bend the magnetization phase, thereby enlarging (and enhancing) the imaging focus region of the subject in the phase-encoding direction. Such imaging sequences are described in further detail below. 
         [0056]    The imaging sequence controller  6  can obtain one or more image sequence algorithms from the imaging sequence memory and control one or more of a magnetic field gradient controller module  4 , a radio frequency (RF) pulse controller module  7 , an analog/digital (A/D) signal converter module  10 , and the image reconstruction module  11  in order to effect the application of RF and field gradient pulses. 
         [0057]    The image reconstruction module  11  can communicate with the analog/digital (A/D) signal converter module  10  to receive digital images of the subject. The image reconstruction module can store these images in an image memory module  26 , image storage module  12 , and/or image processing memory module  13 . 
         [0058]    As will be appreciated by one of ordinary skill in the art, the various modules described herein can be distinct hardware and/or software modules or can be combined into one or more hardware and/or software modules. For example, the magnetic field gradient controller module  4 , radio frequency (RF) pulse controller module  7 , and analog/digital (A/D) signal converter module  10  can be interfaces provided and incorporated within the MRI device  1  while the imaging sequence controller  6  is external to the MRI device  1 . Alternatively, the imaging sequence controller  6  can be incorporated within the MRI device  1 . 
       Magnetization Phase-Bending at Imaging Focus 
       [0059]    To magnify the regions of interest in a MRI image (hereinafter referred to as “imaging focus” or “imaging foci”), a phase encoding method, as described herein, uses specially designed radiofrequency pulses to interact with magnetic field gradients, such that the magnetization phase at a predefined focus or foci is bent precisely as prescribed. The MRI techniques of the present disclosure (hereinafter referred to as “magnetic resonance magnification imaging” or “magnification imaging”) therefore lie outside the realm of k-space theory which applies to phase encoding using field gradients only. By successively bending the phase of electromagnetic signals from imaging focus during phase-encoding, the differential phase evolution at imaging focus will be faster than in conventional MRI. Since Fourier transform image reconstruction evenly divides the phase space into pixels, which is automatically performed when generating the raw magnified image of the k-space data, the imaging focus will be filled with more pixels than in conventional MRI, leading to focal resolution enhancement in a manner similar to optical magnification. Because phase encoding is one of the most time-consuming parts of MRI, magnetic resonance magnification imaging reduces scan time for a predefined focal spatial resolution. Or equivalently, it increases spatial resolution at imaging focus for the same scan time. 
         [0060]    By evenly skipping phase encoding steps, as in PPI, as described above, or by over-bending the focal magnetization phase, the magnified image will be folded. The folded image can be unfolded using conventional PPI methods. Therefore, magnification imaging is compatible with both image domain and k-space domain PPI methods. 
         [0061]    The magnification imaging techniques described herein are based on specific interactions between magnetic field gradients used in conventional MRI and specially designed radiofrequency pulses to bend magnetization phase at the imaging focus. To design the phase-bending radiofrequency pulses, one or more of the following steps may be performed:
       1. Specify the position of imaging focus and the length of aperture stop inside the image field-of-view (FOV).   2. Design a smoothly-varying monotonic magnetization phase curve from −π to π as the phase module. The phase derivative at imaging focus is specified by the desired magnification. The phase module bends at the two sides of the aperture.   3. Design a trapezoid magnetization amplitude module with its two top vertices smoothed. The flat top of the trapezoid matches the image FOV.   4. Extend the phase module at both ends to match the bottom two vertices of the amplitude module.   5. Use Fourier transform, or other mathematical methods, to design radiofrequency pulses. The magnitude of the frequency response of the radiofrequency pulses will match the magnitude module; the phase of the frequency response of the radiofrequency pulses will match σ x phase module, where σ denotes the phase encoding count. For example, for 128 phase encoding steps, σ=−64˜63 or −63˜64.       
 
         [0067]    Referring now to  FIG. 1 , shows examples of complex radiofrequency pulses that bend magnetization phase. The top trace shows a Bloch simulation of amplitude- and phase-modulated radiofrequency pulses which bend the magnetization phase at a predefined imaging focus (focus position: pt#620; left panels: σ=−2; right panels: σ=64). The middle and bottom traces show the amplitude and phase of the excited transverse magnetization. The middle trace shows transverse magnetization magnitude while the bottom trace shows transverse magnetization phase in radians. For the examples shown in  FIG. 1 , the imaging focus is centered at point #620 with a magnifying power of 2×. By this method, differential phase evolution of magnetization at the imaging focus is made faster than conventional MRI. 
       Magnification Imaging and Reconstruction 
       [0068]    Magnification imaging, as described herein, can be described as a “two-step” process, although in reality, it is actually achieved in a single step. To this end, in the first step, the object to be imaged may be virtually and precisely “stretched” at the imaging focus region in the phase-encoding direction to expose its fine details there accompanied by reduced spin density. The object stretching is the result of bending the magnetization phase using the specially designed radiofrequency pulses. In the second step, an MRI imaging sequence (e.g., a conventional MRI imaging sequence) may be used to image the stretched object, followed by reconstruction using Fourier transform, or any other mathematical model, to generate the raw magnified image. Since the origin of each pixel is determined by the predefined magnetization phase module, two different exemplary methods can be used to regrid the raw magnified image:
       1. Mathematically invert the stretching process; or   2. Experimentally measure the magnetization magnitude and phase modules on an imaging phantom (e.g., an object that is scanned or imaged to evaluate, analyze, and/or tune the performance of an imaging device) (hereinafter “phantom”).       
 
         [0071]    For better visualization, the regridded image can be displayed using evenly spaced pixels. Regridding error can be made arbitrarily small by increasing the reconstructed image matrix size in the phase encoding direction. Finally, if necessary, the image can be smoothed by standard image processing methods. 
       Working Example 1—One-Dimensional Simulation 
       [0072]    In one example of the magnetic resonance magnification imaging techniques disclosed herein,  FIG. 2  illustrates an example of one-dimensional magnification imaging and reconstruction. To this end,  FIG. 2  compares: a ground truth image (from top: 1st trace); a reconstructed image using conventional MRI (2nd trace; 128 points), where the fine details were largely lost due to limited spatial resolution; and a raw magnified image generated using 128 bent-phase profiles (two were shown in  FIG. 1  for phase encoding #63 (σ=−2) and 128 (σ=64), respectively) (3rd trace; 128 points, 2× magnification, focus position: 0.12× field-of-view). After intensity correction and “regridding” to 128×128 points, the magnified image is shown in the bottom trace (4th trace) overlaid onto the ground truth image (no smoothing is performed for better visualization of focal spatial resolution enhancement). Clearly, with the same number of phase-encoding steps, focal magnification captured the fine structure around 0.12× field-of-view. 
       Working Examples 2 and 3—Phantom Experiments 
       [0073]    In additional examples of the magnetic resonance magnification imaging techniques disclosed herein,  FIGS. 3 and 4  illustrate axial images of phantoms that were acquired using a Bruker 11.7 Tesla 89-mm vertical bore magnet equipped with a single proton channel and a 38-mm i.d. birdcage coil. Referring now to  FIG. 3 , the top left panel shows a conventional spin echo image of a tube phantom with a comb-like insert using a sinc excitation pulse. Matrix size=256×128. Phase encoding (128 steps) is along the left-right direction. The top middle panel shows the raw magnified image with 2× magnifying power and 128 phase encoding steps. The imaging focus was placed at the center groove. Focal magnification effect is clearly seen. The top right panel shows the “regridded” to 8192 in phase encoding direction with no smoothing. The bottom panel shows the one-dimensional profile of the center line across the grooves (top graph), where the center groove was defined by two pixels (middle graph). In the magnified regridded image the center groove was defined by four pixels (bottom graph). 
         [0074]      FIGS. 4A-4C  give another phantom example. Similar to  FIG. 3 , the imaging focus is placed at the syringe in the center.  FIG. 4A  illustrates a conventional image with a slice thickness of 2 mm, field of view of 32 mm and matrix size of 256×128.  FIG. 4B  is a raw magnified image using 128 phase-bending radiofrequency pulses with a magnifying power of 2×.  FIG. 4C  is a regridded image to 8192 in phase encoding direction. The edges of the syringe were sharpened in the magnified image ( FIG. 3C ), although the number of phase encoding steps (e.g., 128) is the same as in the conventional image ( FIG. 3A ). 
       Working Examples 4 and 5—In Vivo Experiments 
       [0075]    In additional examples of the magnetic resonance magnification imaging techniques disclosed herein,  FIGS. 5 and 6  illustrate examples of in vivo applications of the magnification imaging technique. In this regard, adult rats are imaged at 11.7 Tesla under 1.5% isoflurane anesthesia using a 15-mm single-loop transceiver surface coil (studies conducted under a protocol approved by NIMH Animal Care and Utilization Committee). 
         [0076]    Referring now to  FIGS. 5A-5D , a conventional horizontal image of a rat brain is shown in the top-left panel ( FIG. 5A ). With the imaging focus placed at the brain midline (magnifying power: 2×), anatomical details along the brain midline are better resolved as shown in  FIG. 5B  (raw magnified image) and  FIG. 5C  (regridded magnified image). Meanwhile,  FIG. 5D  shows a comparison of the olfactory bulb/cerebral cortex area. The anatomical details are better defined in the magnified image ( FIG. 5B ) than in the conventional MRI image ( FIG. 5A ). 
         [0077]      FIGS. 6A-6B  compare the conventional image of a horizontal slice of rat brain ( FIG. 6A ) with the magnified image of the same slice generated in accordance with the techniques disclosed herein ( FIG. 6B ). The imaging focus is placed at brain midline with a magnifying power of 3×. Fine anatomical structures along the midline are sharpened by magnification imaging. Notably, the aqueduct of Sylvius at the superior colliculus is visible in the magnified image only. 
       Working Example 6—Two-Dimensional Simulation 
       [0078]    In another example of the magnetic resonance magnification imaging techniques disclosed herein,  FIG. 7  demonstrates the combination of magnification imaging and PPI using a simulated phantom with three thin bars at its right edge. To this point,  FIG. 7  shows that resolution enhancement from these two independent approaches multiplies (e.g., two-fold enhancement by PPI× two-fold enhancement by magnification imaging results in four-fold resolution enhancement). Since magnification imaging uses Fourier transform, or other similar mathematic formulae, for reconstruction, the magnified image can be folded and unfolded as in conventional PPI. 
         [0079]    Referring to  FIGS. 7A-7E ,  FIG. 7A  illustrates a ground truth image while  FIG. 7B  shows an unfolded image reconstructed from eight folded images using conventional PPI. The 2× acceleration is along the left-right direction. The three bars at the right edge are not resolved due to limited spatial resolution. The middle panels show an individual folded magnified image and the unfolded raw magnified image.  FIG. 7C  is a folded magnified image from one individual coil,  FIG. 7D  is an unfolded raw magnified image using conventional PPI reconstruction and  FIG. 7E  is a regridded magnified PPI image. The imaging focus is placed at the right edge of the phantom. Due to 2× magnification, the three bars at the right edge are resolved. The raw magnified image may be unfolded using conventional PPI. The raw magnified image may then be regridded to generate a normal image ( FIG. 7E ). By combining magnification imaging with PPI, the spatial resolution at the right edge can be increased by 300% (2×2=4). 
       Working Example 7—Four-Fold Magnification 
       [0080]    Radiofrequency pulses using inverse Fourier transform can be designed to produce 4× magnification.  FIG. 12  shows an example of 4× magnification imaging of a phantom with three teeth. The imaging focus was placed at the center tooth. Slice thickness is 2 mm, field of view is 32 mm and matrix size is 512×128. The image was regridded to 8192. Focal magnification effect was clearly seen in the 2D image where the edges of the center tooth were dramatically sharpened due to 4-fold focal magnification. In comparison, the left and right teeth were blurry due to lower spatial resolution there. 
         [0081]    Multi-Foci Magnification Imaging 
         [0082]    The magnetic magnification imaging techniques of the present disclosure may further incorporate multi-foci imaging. In particular, a double foci magnification technique may be utilized where the differential magnetization phase at the two edges of the field-of-view can be made to evolve faster than conventional MRI. This may lead to increased spatial resolution at the two sides of the field-of-view. Two or more imaging foci may be established at locations of anatomical interest. For example,  FIG. 13  shows an image of a phantom containing a bundle of thin tubes with the same wall thickness. Slice thickness is 2 mm, field of view 32 mm and matrix size 256×128. Both the left and right sides of the bundle are magnified. Although the small tubes in the middle of the image are of low resolution the ones on both sides are much better resolved because of double-foci magnification. Spatial resolution at different imaging foci can be varied depending on desired spatial resolution. It is envisioned that the magnetic resonance imaging devices can incorporate a user-friendly interface that allows a user to prescribe multiple foci at locations of anatomical interest by drawing on scout images. 
       CONCLUSION 
       [0083]    Accordingly, the magnetic resonance magnification imaging techniques disclosed herein use a fundamentally different approach to MRI image formation. In particular, specially designed radiofrequency pulses can interact with the magnetic field gradient(s) such that the region of interest is filled with more pixels, thereby increasing spatial resolution at the region of interest. 
         [0000]    Implementation in Hardware and/or Software 
         [0084]    The methods described herein can be implemented on specially-programmed hardware or software. For example, the methods can be implemented by a computer-readable medium. The computer-readable medium can be non-transitory and/or tangible. For example, the computer readable medium can be volatile memory (e.g., random access memory and the like) or non-volatile memory (e.g., read-only memory, hard disks, floppy discs, magnetic tape, optical discs, paper table, punch cards, and the like). 
       EQUIVALENTS 
       [0085]    While the present subject matter has been described with reference to the above embodiments, it will be understood by those skilled in the art that various changes can be made and equivalents can be substituted for elements thereof without departing from the scope of the subject matter. In addition, many modifications can be made to adapt a particular situation or material to the teachings of the subject matter without departing from the essential scope thereof. Therefore, it is intended that the subject matter not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out this subject matter, but that the subject matter will include all embodiments falling within the scope of the appended claims. 
         [0086]    The functions of several elements may, in alternative embodiments, be carried out by fewer elements, or a single element. Similarly, in some embodiments, any functional element may perform fewer, or different, operations than those described with respect to the illustrated embodiment. Also, functional elements (e.g., modules, databases, computers, clients, servers and the like) shown as distinct for purposes of illustration may be incorporated within other functional elements, separated in different hardware or distributed in a particular implementation. 
         [0087]    While certain embodiments according to the present subject matter have been described, the present subject matter is not limited to just the described embodiments. Various changes and/or modifications can be made to any of the described embodiments without departing from the spirit or scope of the present subject matter. Also, various combinations of elements, steps, features, and/or aspects of the described embodiments are possible and contemplated even if such combinations are not expressly identified herein.