Patent Publication Number: US-9897677-B2

Title: Method for correcting errors associated with asynchronous timing offsets between transmit and receive clocks in MRI wireless radiofrequency coils

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) AND CLAIM OF PRIORITY 
     The present application claims priority to U.S. Provisional Patent Application Ser. No. 61/873,725, filed Sep. 4, 2013, entitled “METHOD FOR CORRECTING ERRORS ASSOCIATED WITH ASYNCHRONOUS TIMING OFFSETS BETWEEN TRANSMIT AND RECEIVE CLOCKS IN MRI WIRELESS RADIOFREQUENCY COILS” and U.S. Provisional Patent Application Ser. No. 61/923,125, filed Jan. 2, 2014, entitled “WIRELESS MRI RADIO FREQUENCY COILS AND PULSE SEQUENCES FOR ON-BOARD PROSPECTIVE MOTION DETECTION AND CORRECTION”. The content of the above-identified patent documents are incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present application relates generally to methods and apparatuses for signal correction and, more specifically, to correct timing between transmit and receive clocks for wireless radiofrequency coils in a magnetic resonance imaging system. 
     BACKGROUND 
     Magnetic resonance imaging (MRI) is a modality for evaluating tissue structure and function. Several MRI techniques are routinely used in clinical and research settings to answer questions related to anatomy, physiology and pathology at acute and chronic disease stages. Of the many developmental sub-fields in MRI, one of the more rapidly growing areas concerns multi-channel radio frequency (RF) coils for signal transmission and/or reception. In particular, over the past decade, there has been widespread interest in implementing wireless RF solutions owing to several problems associated with wired RF coils. 
     Firstly, coaxial cables in wired RF coils impart a level of rigidity to the setup process and restrict the range of motion of both, the transmit-receive (Tx-Rx) and Rx-only coil components during setup. Along these lines, with increasing number of arrays (up to 128 channels), cable management becomes very complex. Baluns are required for each channel and cables must be routed efficiently in order to minimize coil interactions. Secondly, due to the switching of coil components in the course of a routine day on a clinical scanner (given the different anatomical body parts examined), the cables are also subject to induced stress over time compromising their elasticity, leading to increased wear and tear and potentially requiring frequent replacements. Thirdly, coaxial cables can play the role of an antenna capturing external noise and lead to a decrease in signal-to-noise ratio (SNR) of the acquired images. For these main reasons, implementing a wireless mode for the RF subsystem is highly desirable. 
     SUMMARY 
     An apparatus is provided for correcting errors associated with timing offsets in radiofrequency coils. The apparatus includes a memory element and a controller. The controller is configured to execute a set of instructions to receive data of a plurality of signals, the plurality of signals comprising at least one projection echo. The controller is also configured to identify a plurality of offsets of the plurality of signals based on the at least one projection echo. The controller is also configured to apply the plurality of offsets to a k-space of the plurality of signals. 
     A method is provided for correcting errors associated with timing offsets in radiofrequency coils. The method includes receiving data of a plurality of signals, the plurality of signals comprising at least one projection echo. The method also includes identifying a plurality of offsets of the plurality of signals based on at least one projection echo. The method also includes applying the plurality of offsets to a k-space of the plurality of signals. 
     A non-transitory computer-readable storage medium comprising logic, stored on the computer-readable storage medium for execution on a plurality of processors is provided for correcting errors associated with timing offsets in radiofrequency coils. The logic includes receiving data of a plurality of signals, the plurality of signals comprising at least one projection echo. The logic also includes identifying a plurality of offsets of the plurality of signals based on at least one projection echo. The logic also includes applying the plurality of offsets to a k-space of the plurality of signals. 
     Before undertaking the DETAILED DESCRIPTION below, it may be advantageous to set forth definitions of certain words and phrases used throughout this patent document: the terms “include” and “comprise,” as well as derivatives thereof, mean inclusion without limitation; the term “or,” is inclusive, meaning and/or; the phrases “associated with” and “associated therewith,” as well as derivatives thereof, may mean to include, be included within, interconnect with, contain, be contained within, connect to or with, couple to or with, be communicable with, cooperate with, interleave, juxtapose, be proximate to, be bound to or with, have, have a property of, or the like; and the term “controller” means any device, system or part thereof that controls at least one operation, such a device may be implemented in hardware, firmware or software, or some combination of at least two of the same. It should be noted that the functionality associated with any particular controller may be centralized or distributed, whether locally or remotely. Definitions for certain words and phrases are provided throughout this patent document, those of ordinary skill in the art should understand that in many, if not most instances, such definitions apply to prior, as well as future uses of such defined words and phrases. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present disclosure and its advantages, reference is now made to the following description taken in conjunction with the accompanying drawings, in which like reference numerals represent like parts: 
         FIG. 1  illustrates an MRI system in accordance with an embodiment of this disclosure; 
         FIG. 2  illustrates an example processing device in a computing system according to this disclosure; 
         FIG. 3  illustrates a Tx-Rx sub-system in accordance with an embodiment of this disclosure; 
         FIG. 4  illustrates a diagram of a 2D spin echo sequence in accordance with an embodiment of this disclosure; 
         FIG. 5  illustrates a diagram of a spin echo pulse sequence with a navigator module in accordance with an embodiment of this disclosure; 
         FIG. 6  illustrates a process for navigator echo based correction of a clock mismatch according to an embodiment of this disclosure; 
         FIGS. 7A-7E  illustrate a process for identifying an image shift and remedying such shifts in accordance with an embodiment of this disclosure; 
         FIG. 8  illustrates different levels of skew correction in k-space and k-space via navigator echoes in accordance with an embodiment of this disclosure; 
         FIG. 9  illustrates a plot of the noise level against an absolute error following navigator echo-based corrections of k-space skews from two sample frequency mismatch conditions (100 ppb and 1 ppm) over several noise levels defined as peak noise over peak k-space signal in accordance with an embodiment of this disclosure; 
         FIG. 10  illustrates a process for correcting an MRI image in accordance with an embodiment of this disclosure; and 
         FIG. 11  illustrates a motion detection process in accordance with an embodiment of this disclosure. 
     
    
    
     DETAILED DESCRIPTION 
       FIGS. 1 through 11 , discussed below, and the various embodiments used to describe the principles of the present disclosure in this patent document are by way of illustration only and should not be construed in any way to limit the scope of the disclosure. Those skilled in the art will understand that the principles of the present disclosure may be implemented in any suitably arranged system or method. 
       FIG. 1  illustrates an MRI system in accordance with an embodiment of this disclosure. The MRI system  100  operates a medical imaging technique used in radiology to investigate the anatomy and physiology of the body in both health and disease. MRI scanners use strong magnetic fields and radio waves to form images of the body. The body may be referred to as the tissue, subject, sample, and/or object herein. The MRI system  100  includes components such as a magnet  102 , gradient coils  104 , RF coils  106 , gradient amplifiers  108 , a gradient pulse programmer  110 , an RF detector  112 , a digitizer  114 , an RF amplifier  116 , a pulse programmer  118 , an RF source  120 , a computing system  122 , and a display  124 , as described below. The embodiment of the MRI system  100  shown in  FIG. 1  is for illustration only. Other embodiments of an MRI system could be used without departing from the scope of the present disclosure. 
     The magnet  102  may be an electromagnet (such as a superconducting and/or resistive magnet), permanent magnet, and/or the like. The magnet  102  forms a strong magnetic field around the area to be imaged. In one or more embodiments, in operational terminology, the magnet  102  may be a Helmholtz coil pair driven by a power supply to generate a stable, homogeneous static main magnetic field along the z-axis for polarizing nuclei. 
     The gradient coils  104  may also be electromagnets (such as a superconducting and/or resistive), permanent magnets, and/or the like. The gradient coils  104  are used to spatially encode the positions of protons by varying the magnetic field linearly across the imaging volume. In one or more embodiments, in operational terminology, three sets of gradient coils  104  driven by gradient field coil drivers create inhomogeneous linear gradient magnetic fields along x, y, and z axes that are used for spatial localization of the MRI signals. 
     The RF coils  106  may also be used as receiving (Rx) coils, and in an embodiment, depending on the filling factor desired. The RF coils  106  pick up the RF electromagnetic radiation produced by nuclear relaxation inside the subject. The RF coils  106  now operate as a Rx coil given that this phenomenon occurs following excitation (by means of RF coils  106 ) and signal reception is now performed by the Rx coil which could also serve as a function of the Tx coil, thereby making such as coil a transceiver. The RF coils  106  can serve as Rx and Tx coils. In other embodiments, the Rx and Tx coils may be separated. 
     In one or more embodiments, in operational terminology, the RF coils  106  which generate time varying and rotating magnetic fields required to excite nuclei and measure MR signals, are positioned within the setup of the magnet  102  and gradient coils  104 . The sample under examination is placed within the RF coils  106 . The RF amplifier  116  is configured to deposit current into the RF coils  106  behaving as a transmitter which generates an RF field. The RF field applies a torque to the nuclear magnetization of the sample, more specifically, hydrogen molecules in the sample. 
     The driving time of each of the gradient coils  104  and timing of RF field generation is overseen by the computing system  122  according to a programmed sequence of events by the pulse programmer  118 , referred to as a pulse sequence. The RF field can induce an electromotive force (EMF) in RF receiver Rx coils which is sent to a signal processor through a pre-amplifier and phase sensitive detector. The received data are then processed and converted into images. Hence, RF coils can serve the function of nuclear spin excitation and signal reception. The course of signal transmission at excitation leads to amplification of the signal by the power amplifier to several KW and then transmission of the signal to the RF coil. At reception, the detected signal from the sample is amplified by several μV by the pre-amplifier and then transmission to the phase sensitive detector. In both cases, signal transmission is traditionally carried out using coaxial cables. 
     The computing system  122  represents any suitable computing or processing device. The computing system  122  can interact with a server or other computing device(s) over a network. In this example, the computing system  122  can include a desktop computer, a mobile telephone or smartphone, a personal digital assistant (PDA), a laptop computer, and a tablet computer. However, any other or additional Processing device could be used in the MRI system  100 . 
     Although  FIG. 1  illustrates one example of an MRI system  100 , various changes may be made to  FIG. 1 . For example, the MRI system  100  could include any number of each component in any suitable arrangement. In general, MRI systems come in a wide variety of configurations, and  FIG. 1  does not limit the scope of this disclosure to any particular configuration. While  FIG. 1  illustrates one operational environment in which various features disclosed in this patent document can be used, these features could be used in any other suitable system. 
     The basic hardware components of all MRI systems are the magnet (permanent or superconducting) producing a stable and very intense magnetic field, the gradient coils creating a variable field and to encode spatial positioning, and radio frequency (RF) coils which are used to transmit energy, and to detect material/tissue resonance induced radiated RF signal. A computer controls the MRI scanning operation and processes the information. 
     RF coils are large inductors (wire or trace looped around the core of the coil) with a considerable dimension and a defined wavelength. Coils are used to create a magnetic field or to detect a changing magnetic field by voltage induced in the wire. A coil is usually a small antenna. RF coils can be differentiated by their function into three general categories: 1) Transmit (Tx)-only, 2) Receive (Rx)-only, and 3) Tx-Rx coils. In MRI, RF coils in different shapes and sizes are used for different body parts and to handle individual applications. Depending on the anatomy of interest, these coils fall into either the volume coil or a surface coil categories. Volume coils comprise birdcages, circularly polarized coils, crossed coils, Helmholtz pair, paired saddle coils and single turn coils. Surface coils consist of phased-arrays, body wrap-around coils and linearly polarized coils. The RF signal is in the range of 10 to 300 MHz deemed to be safe on clinical whole body scanners. During typical clinical imaging scans, the entire frequency spectrum of interest is on the order 10 kHz-1 MHz, which is an extremely narrow band, considering that the center frequency is about 100 MHz. 
       FIG. 2  illustrates an example processing device  210  in a computing system  200  according to this disclosure. The computing system  200  could represent the computing system  122  in  FIG. 1 . 
     As shown in  FIG. 2 , the computing system  200  includes a bus system  205 , which supports communication between at least one processing device  210 , at least one storage device  215 , at least one communications unit  220 , and at least one input/output (I/O) unit  225 . 
     The processing device  210  executes instructions that may be loaded into a memory  230 . The processing device  210  may include any suitable number(s) and type(s) of processors or other devices in any suitable arrangement. Example types of processing devices  210  include controllers, microprocessors, microcontrollers, digital signal processors, field programmable gate arrays, application specific integrated circuits, and discreet circuitry. 
     The memory  230  and a persistent storage  235  are examples of storage devices  215 , which represent any structure(s) capable of storing and facilitating retrieval of information (such as data, program code, and/or other suitable information on a temporary or permanent basis). The memory  230  may represent a random access memory or any other suitable volatile or non-volatile storage device(s). The persistent storage  235  may contain one or more components or devices supporting longer-term storage of data, such as a ready only memory, hard drive, Flash memory, or optical disc. 
     The communications unit  220  supports communications with other systems or devices. For example, the communications unit  220  could include a network interface card or a wireless transceiver facilitating communications over a network. The communications unit  220  may support communications through any suitable physical or wireless communication link(s). 
     The I/O unit  225  allows for input and output of data. For example, the I/O unit  225  may provide a connection for user input through a keyboard, mouse, keypad, touchscreen, or other suitable input device. The I/O unit  225  may also send output to a display, printer, or other suitable output device. 
     One or more embodiments of this disclosure recognize and take into account that one of the primary challenges in implementing a wireless RF coil solution is synchronization between the RF Tx and Rx signals. Poor synchronization can result in image quality deterioration owing to phase rotation due to frequency mismatch between Tx and Rx clocks. In current systems, the receiver was connected to the MR system clock and the transmitter sent signals wirelessly. Hence, this system does not involve a fully wireless Rx system. An alternative proposal entailed using a bi-directional wireless link where the digitized MR signal was sent from the Rx coil to the MR system and a clock signal was routed in the opposite direction. The system entailed an amplitude modulation transmitter where a 2.4 gigaHertz (GHz) carrier was modulated with 2 megaHertz (MHz) clock sourced from the existing system and an envelope-detection based receiver. Although in this system the phase errors may be low, given that the transmitter clock is inherently noisy, the receiver could become asynchronous. This could lead to random displacements in the nuclear magnetic resonance (NMR) Fourier space or k-space from one line to the next line of each data readout. Such errors may extend beyond the scope of an effective correction. Furthermore, there may be additional k-space errors and resultant image domain artifacts. 
     Another system is a two-pronged system for transmitting a pilot signal together with the MR signal. One approach here is to broadcast the pilot signal with an offset in frequency but near the free induction decay (FID) frequency. A transponder in the receiver can then up convert the pilot signal along with the FID signal for transmission. The received pilot signal then serves as a phase reference for the image data with pilot phase variations being subtracted in the FID signal. Here, despite the proposed subtractions, phase error accumulation may not be easily resolved, especially in the presence of increasing system noise. Furthermore, the level of system noise could govern the accuracy of the received pilot signals. Inaccuracies here may lead to a shift of k-space locations from one line to the next data readout line and would require an effective post-processing correction. A second transmission approach focuses on up converting the FID and pilot signal by amplitude modulations, with a single side band of the modulated carrier signal being transmitted to the processing unit which recovers both the pilot and FID signal by demodulation. The pilot and FID are then mixed to get a difference signal with phase error cancellation. The difference signal can then be down converted as required to obtain the FID signal. Also, phase error accumulation may not be readily resolved and could result in phase shift that causes blurring across images. 
     One or more embodiments of this disclosure provide an error correction method that can remedy image artifacts associated with timing offsets between transmit and receive clocks in wireless RF coil setups for MRI scans. Unlike previous systems, this disclosure provides for a non-hardware level solution. Given the nature of the expected errors due to Tx and Rx clock frequency mismatch, the system and methods in one or more embodiments of this disclosure acquire extra data without significantly lengthening scan acquisition times to be utilized for adjusting the effects of the offsets in the raw data. In an example embodiment, the systems and methods provide a retrospective solution. 
     One or more of the embodiments in this disclosure relate towards nuclear magnetic resonance inspection equipment. In particular, a MRI scanner for visualizing and post-processing a density distribution of nuclei including relaxation time distributions by measuring induced MR signals from magnetic nuclei such as hydrogen from biological tissues. These phenomena are linked to radiofrequency (RF) coils that are used to generate and/or receive time-varying RF magnetic fields. 
       FIG. 3  illustrates a Tx-Rx sub-system in accordance with an embodiment of this disclosure. The Tx-Rx sub-system  300  is a part of the MRI system  100 . MRI scanners use strong magnetic fields and radio waves to form images of the body. The Tx-Rx sub-system  300  comprises the RF coils  106  and components used to utilize the RF coils  106  and analyze the data received by the RF coils  106 . The Tx-Rx sub-system  300  includes components such as, the RF coils  106 , RF amplifier  116 , computing system  122 , a transmitter/receiver (T/R) switch  302 , a pre-amplifier  304 , a mixer  306 , a local oscillator  308  with a PTS frequency synthesizer, a BP filter/amplifier  310 , and an analog-to-digital converter  312 . The embodiment of the Tx-Rx sub-system  300  shown in  FIG. 3  is for illustration only. Other embodiments of a Tx-Rx sub-system could be used without departing from the scope of the present disclosure. 
       FIG. 4  illustrates a diagram of a 2D spin echo sequence  400  in accordance with an embodiment of this disclosure. The spin echo sequence  400  is made up of a series of events: 90° excitation pulse  402 , 180° refocusing pulse  404  at TE/2, and DRO  406  at TE. This series of events is repeated at each time interval TR (Repetition time). With each repetition, a k-space line is filled, according to a variation in the phase encoding gradient. The 180° refocusing pulse  404  compensates for the constant field heterogeneities to obtain an echo that is weighted in T2 and not in T2*. The embodiment of the spin echo sequence  400  shown in  FIG. 4  is for illustration only. Other embodiments of a spin echo sequence could be used without departing from the scope of the present disclosure. Additionally, in an example,  FIG. 4  includes a spin echo (not depicted) similar to spin echo  502  as shown in  FIG. 5 . 
     The gradients include a slice select gradient  408 , phase-encoding gradient  410 , and frequency-encoding gradient  412 . The spin echo sequence  400  shows an example sequence where the 180° refocusing pulse  404  inverts the plane of transverse magnetization thereby reversing time-independent field variations that lead to signal dephasing (as seen in gradient recalled echo or “GRE” imaging). These methods are characterized by the frequency-encoding gradient  412  being switched on during data acquisition causing the resonant frequency to become a function of location. The composite signal is then analyzed by means of a Fourier transform that decomposes signal intensities of distinct frequency components to certain locations. 
     In the second dimension perpendicular to the frequency-encoding gradient  412 , the information about the position of the magnetization vector (phase) is used for encoding spatial information. The phase-encoding gradient  410  is first switched on briefly to establish a difference in phase positions for the magnetization vectors within each voxel in the direction of the magnetic field gradient. This is followed by application of the frequency-encoding gradient  412 . 
     The time between adjacent points (or lines of frequency encoding points) along the phase encode direction is equal to TR since the signal whose T2 is in most cases longer than the 5 to 10 millisecond (ms) readout period, must be reformed in the interval between the accumulation of each readout line in k-space. In an example, the phase encoding gradient can be pulsed briefly, displacing the signal in the Ky or the phase direction in the NMR Fourier space or K-space and the readout process is repeated. The cycle consisting of an excitation followed by phase encode followed by readout is repeated until the desired net displacement (or spatial resolution) along the phase encode axis is achieved. In the conventional K-space diagram, raw data lines are collected one at a time separated by a TR period ranging from 10 ms to 3000 ms. The measurement time is equal to the number of phase encoding steps multiplied by the TR and multiplied by the number of acquisitions (or averages). 
     In an embodiment, in operational terminology, a spin echo sequence has two essential parameters: TR and TE. TR is the time interval between two successive 90° excitation RF pulses. It conditions the longitudinal relaxation of the explored tissues (depending on T1). The longer the TR, the more complete the longitudinal magnetization regrowth (Mz tends to M0). Reducing TR will weigh the image in T1 as the differences between the longitudinal relaxations of the tissues&#39; magnetization will be highlighted. In classic spin echo, after TR time, a single k-space line will be acquired. TR repetition is thus responsible for the duration of the sequence. TE is the time interval between the 90° flip angle and receipt of the echo, the signal being produced by transverse magnetization. Transverse magnetization decreases according to the time constant T2 of each sample (the field heterogeneities [which contribute to T2*effects] being compensated by the 180° flip angle applied at TE/2). 
     One or more embodiments of this disclosure recognize and take into account that wireless RF coils afford a more practical solution devoid of many of the aforementioned issues pertaining to cable management. Nonetheless, in a wireless RF coil setup, if the Tx and Rx clocks are not well synchronized or suffer poor synchronization, this can lead to phase encode jitters or offsets in MR images. 
     One or more embodiments of this disclosure recognize and take into account that in conventional MRIs (using wired RF setups), a Fourier transform analysis of the recorded time domain signal can help recover the magnetization at each frequency or position during the application of gradients. In spatial encoding, an x and a y gradient (G x , G y ) are applied to a spin system in order to perform frequency and phase encoding, respectively. The receiver coil spans the extent of the sample and the detected signal S(t) is given by integrating the magnetization given by I(x, y, z 0 ) over the range of x and y positions as,
 
 S ( t )= S ( k   x   ,k   y )=∫ −∞   +∞ ∫ −∞   +∞   I ( x,y,z   0 ) e   jk     y     y   e   jk     x     x   dxdy,   (1)
 
where
 
 k   x   =γG   x   t,   (2)
 
 k   y   =γG   y   T   p ,  (3)
 
and
 
                     (     x   ,   y   ,     z   0       )     =         j   ⁢           ⁢     ω   0     ⁢   Δ   ⁢           ⁢   z       2       ⁢       M   xy   0     ⁡     (     x   ,   y   ,     z   0       )       ⁢       B     1   ⁢           ⁢   T       ⁡     (     x   ,   y   ,     z   0       )       ⁢       e     -     t     T   2           .               (   4   )               
In the above equations, k x  and k y  are the k-space locations, T p  is the phase encoding duration, Δz is the slice thickness, M xy   0  is the initial magnetization in the xy plane, ω 0  is a Larmor frequency, and B 1T  is the RF field strength. In an example, ω 0 =γB 0 , where γ is the gyromagnetic ratio and B 0  is the static magnetic field strength.
 
     The clock mismatch can mainly be attributed to a Δt term that arises due to a constant offset that is dependent on the frequency offset between the clocks designated for Tx and Rx functions in the wireless RF MRI realm. 
     The detected signal can now be expressed as, 
                     S   ⁡     (     t   +     Δ   ⁢           ⁢   t       )       =       ∫     -   ∞       +   ∞       ⁢       ∫     -   ∞       +   ∞       ⁢       I   ⁡     (     x   ,   y   ,     z   0       )       ⁢           ⁢     e     j   ⁢           ⁢     k   y     ⁢   y       ⁢     e     j   ⁢           ⁢     k   x     ⁢   x       ⁢     e     -       Δ   ⁢           ⁢   t       T   2           ⁢     e     j   ⁢           ⁢   γ   ⁢           ⁢     G   x     ⁢   Δ   ⁢           ⁢   t   ⁢           ⁢   x       ⁢     e     j   ⁢           ⁢   γ   ⁢           ⁢   B   ⁢           ⁢   Δ   ⁢           ⁢   t       ⁢   d   ⁢           ⁢   x   ⁢           ⁢   d   ⁢           ⁢     y   .                   (   5   )               
The terms that take relaxation and k-space offsets into account with Δt have now been incorporated into equation (5). The term
 
             e     -       Δ   ⁢           ⁢   t       T   2               
is related to the offset between the frequency encoding gradient and acquisition window resulting in T 2  filtering effects which lead to signal cancellation. The term e jγG     x     Δtx  is also related to the offset between the frequency encoding gradient and acquisition window, but leads to a distortion and deformation of the object shape. This effect is coupled to
 
             e     -       Δ   ⁢           ⁢   t       T   2               
above. e jγBΔt  arises from demodulation and leads to a shift of the object within the field-of-view (FOV).
 
     The signal expression is now rewritten as,
 
 S ( t+Δt )= S ( k   x   ′,k   y )=∫ −∞   +∞ ∫ −∞   +∞   I ′( x,y,z   0 ) e   jk     y     y   e   jk′     x     x   e   jγG     x     Δtx   e   jγBΔt   dxdy   (6)
 
where
 
 k   x   ′=γG   x ( t+Δt )  (7)
 
and
 
     
       
         
           
             
               
                 
                   
                     
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     The term of 
             e     -       Δ   ⁢           ⁢   t       T   2               
is related to the offset between frequency-encoding gradient and acquisition window, resulting in a linear shift along the x direction in the image. The term of e jγG     x     Δtx  is related to the offset between frequency-encoding gradient and acquisition window, resulting in shifts of the k-space center and distortions of the object shape. The term e jγBΔt  arises from demodulation, and leads to a shift of the object within the field of view.
 
     A common source of error in MRI is subject motion due to translational or rotational displacements during the course of image acquisition. This can be treated as rigid body motion which can occur randomly during the scan. This results in a linear phase shift along x and y. The most straightforward solution for dealing with translational motion is by using navigator echoes where extra data is acquired within a repetition time (TR) to allow tracking object motion which can then be used to recover the phase shifts and correct the image blurring. A navigator echo, or projection signal, may be additional spin or gradient echoes used to monitor changes in the position of the sample during the scan time (TR). A navigator echo may be one type of projection echo, projection signal, interleaved tracking echo, view tracking echo, and/or object projection in 1D, 2D or 3D. 
     Rigid body translational motion for which all locations of the object undergo identical displacements where the corrupted signal is related to the true signal by
 
 {tilde over (S)} ( k   x   ,k   y )= e   −iφ(k     x     ,k     y     )   S ( k   x   ,k   y )  (9)
 
where s(k x , k y ) is the true uncorrupted signal and the phase is given by
 
φ( k   x   ,k   y )=2π( k   x   Δx,k   y   Δy )  (10)
 
Δx and Δy are applied translational phase shifts in the x and y directions, respectively, for each k-space line.
 
     Navigator echoes provide a cost-effective solution for tracking motion and correcting phase shifts. Prior to each view or phase encode, a non-phase encoded projection (navigator) is acquired in the frequency encoding direction. A single navigator projection is selected as a reference and cross correlation functions are determined with respect to each of the other navigator projections. One approach relies on the maximum of cross-correlation which yields the level of displacement with respect to the reference position. At least two navigators must be acquired to view translational motion in two axes. 
       FIG. 5  illustrates a diagram of a spin echo pulse sequence  500  with a navigator module in accordance with an embodiment of this disclosure. The spin echo sequence  500  is made up of a series of events: the 90° excitation pulse  402 , the 180° refocusing pulse  404  at TE/2, the DRO  406  at TE, spin echo  502 , navigator pulse  504 , and shifted slab navigator signal  506 , spoiler gradient  508 , and object shift detection navigator  510 . This series of events is repeated at each time interval TR. With each repetition, a k-space line is filled, according to a different phase encoding. The embodiment of the spin echo sequence  500  shown in  FIG. 5  is for illustration only. Other embodiments of a spin echo sequence could be used without departing from the scope of the present disclosure. 
     In an embodiment, the sequence  500  has the spin echo  502 . The spin echo  502  is the refocusing of spin magnetization by a pulse of resonant electromagnetic radiation. The refocusing can include spin-spin relaxation (T2) and spin-lattice relaxation (T1). 
     The navigator module with the navigator pulse  504 , a separate excitation pulse, and projection readout can be incorporated within the “dead time” afforded in one TR of any pulse sequence. By alternating the x and y projections,  510 , between successive TRs, an estimate is obtained of object shifts or phase shifts in each direction and correct k-space locations can be determined. During this time, the shifted slab navigator signal  506  is acquired, received, or read out. 
     In an embodiment, the spoiler gradient  508  is a magnetic field gradient pulse applied to effectively remove residual transverse magnetization following the projection signal by producing a rapid variation of its phase along the direction of the gradient. 
     One or more embodiments include hardware-independent solutions that involve the acquisition of navigator echoes as an additional data acquisition module within each TR of the sequence. This solution will enable correction of errors arising from both, phase and frequency mismatch in the wireless RF realm. The navigator technique is widely used to track and correct translational subject-induced motion during MRI scans. Here, these echoes can be used to track the linear phase shifts in k-space and the overall skew, a consequence of TR mismatch between transmit and receive clocks in wireless RF coil implementations. 
       FIG. 6  illustrates a process  600  for navigator echo based correction of a clock mismatch according to an embodiment of this disclosure. The clock mismatch effects arising from linear shifts and a k-space skew. The embodiment of the process  600  shown in  FIG. 6  is for illustration only. Other embodiments of the process  600  could be used without departing from the scope of the present disclosure. 
     The process  600  includes operations associated with navigator echo based correction of clock mismatch effects in MR wireless coil implementations. Following a 1D inverse Fourier transformation, a navigator phase profile is obtained per navigator echo, which relays the response of the transverse (x-y) magnetization vector for each (alternating) projection along x and y per TR. Each navigator phase profile obtained can be incorporated into a linear regression from which a slope or phase estimator can be recovered. A collection of such estimates can then be used to identify the maximum k-space shift and permit correction of such shifts globally over the k-space data. 
     At operation  602 , a controller is configured to identify magnitude and phase representation of the navigator signal in k-space. At operation  604 , the controller is configured to perform an inverse Fourier transformation of the navigator magnitude and phase to obtain image domain based representations. At operation  606 , the controller is configured to select a phase in the image domain based representation. At operation  608 , the controller is configured to plot a linear regression of the selected phase. At step  610 , the controller is configured to calculate a slope or phase estimator (Δ{circumflex over (K)} x   1 ) from the linear regression. A collection of such navigator estimates, Δ{circumflex over (K)} x   1 , Δ{circumflex over (K)} x   2 , Δ{circumflex over (K)} x   L , etc. can be used to identify the maximum k-space shift according to the relationship below: 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       K 
                       ^ 
                     
                   
                   = 
                   
                     
                       1 
                       L 
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         L 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           
                             L 
                             - 
                             1 
                           
                           l 
                         
                         ⁢ 
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             K 
                             ^ 
                           
                           x 
                           l 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     Process  600  permits a correction of the skew or shifts resulting from Tx and Rx clock mismatch in the wireless RF coil implementations. 
       FIGS. 7A-7E  illustrate a process for identifying an image shift and remedying such shifts in accordance with an embodiment of this disclosure.  FIG. 7A  illustrates a diagram  702  of a navigator echo signal in the center k-space line. 
       FIG. 7B  illustrates a diagram  704  with a slope  705  from a simulated navigator phase profile after 1D inverse FFT of  702 . This results from object shifts or displacements during the course of a scan. The slope  705  is analogous to what would be observed and correlates with linear phase shifts in k-space as a result of clock frequency mismatch owing to a mismatch from TR to TR in conventional scans where wireless RF coils are used. 
       FIG. 7C  illustrates a collection  706  of ten navigator phase profiles is shown that yield the slopes associated with shifts from TR to TR. These profiles correlate with the shifted k-space lines from which the slope or the amount of the shift and also the intercept or starting k-space points can be recovered by means of a linear equation of the form, y=ax+b. The actual slope and intercept values for the aforementioned ten navigator phase profiles are given in Table 1. Based on these slope and intercept values for each navigator phase profile, a correction of every k-space line (or globally over the entire k-space skew) can be performed to generate artifact free images as shown in  FIGS. 7D-7E . 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Slope and intercept values for ten select 
               
               
                 navigator phase profiles shown in FIG. 7C. 
               
            
           
           
               
               
               
            
               
                 Navigator 
                   
                   
               
               
                 phase profile 
                 Slope (rad/cm) 
                 Intercept (rad) 
               
               
                   
               
            
           
           
               
               
               
            
               
                 1 
                 0.0000 
                 −0.03 
               
               
                 3 
                 0.0050 
                 −3.51 
               
               
                 5 
                 0.0099 
                 −6.98 
               
               
                 7 
                 0.0148 
                 −10.46 
               
               
                 9 
                 0.0197 
                 −13.94 
               
               
                 11 
                 0.0246 
                 −17.41 
               
               
                 13 
                 0.0295 
                 −20.89 
               
               
                 15 
                 0.0344 
                 −24.36 
               
               
                 17 
                 0.0393 
                 −27.84 
               
               
                 19 
                 0.0442 
                 −31.31 
               
               
                   
               
            
           
         
       
     
       FIG. 7D  illustrates an effect of linear phase shift on a k-space sub-sample  708  of nineteen readouts. Slopes and phase values for lines  1 ,  11  and  19  are displayed from Table 1. 
       FIG. 7E  illustrates a process for image correction using navigator echoes. The k-space skew as seen in  FIG. 7D  results in a shift and distortion of the object in the image domain. The object, in image  710 , can first be re-centered in the field-of-view by multiplying the k-space signal by the intercept or starting point obtained from the navigator phase profiles in image  712 . Next, the slope also obtained from the navigator phase profiles is used to recover the k-space skew or offsets along the phase-encoding axis due to mismatches between the frequency encoding gradient and the acquisition window in image  714 . This second correction adjusts the phase errors that stem from the combined effects of linear phase shift and T2 filtering effects. 
       FIG. 8  illustrates different levels of skew correction in k-space  802  and k-space  804  via navigator echoes in accordance with an embodiment of this disclosure. The navigator echoes are acquired for two different frequency mismatch conditions differing by one order of magnitude (100 ppb in k-space  802  vs. 1 ppm in k-space  804 ) at 3T. For the examples shown, the k-space starting points or the intercepts also differ by an order of magnitude (0.312 in k-space  802  vs. 3.12 rad/cm in k-space  804 ). 
       FIG. 9  illustrates a plot of the noise level against an absolute error following navigator echo-based corrections of k-space skews from two sample frequency mismatch conditions (100 ppb and 1 ppm) over several noise levels defined as peak noise over peak k-space signal in accordance with an embodiment of this disclosure. The data in chart  900  shows that the corrections are independent of the level of frequency mismatch owing to the juxtaposition of curves  902  for 100 ppb and  904  for 1 ppm. Further, even at high noise levels (e.g. 9%), the navigator echo-based correction approach yields robust results based on the absolute error of 0.003 at that noise level. Ideally, Tx and Rx clocks with a frequency mismatch of ˜100 ppb would ensure a minimal offset and thereby result in lower error rates following navigator echo corrections. 
       FIG. 10  illustrates a process  1000  for correcting an MRI image in accordance with an embodiment of this disclosure. The controller here may represent the processing device  210  and the memory element may be the memory  230  in  FIG. 2 . The embodiment of the process  1000  shown in  FIG. 10  is for illustration only. Other embodiments of the process  1000  could be used without departing from the scope of this disclosure. 
     At operation  1002 , a controller is configured to execute a set of instructions to receive data of a plurality of signals. The plurality of signals comprise at least one navigator echo. 
     At operation  1004 , the controller is also configured to identify a plurality of offsets of the plurality of signals based on the at least one navigator echo. The term 
             e     -       Δ   ⁢           ⁢   t       T   2               
is related to the offset between the frequency-encoding gradient and acquisition window resulting in T 2  filtering effects which lead to signal cancellation. The term e jγG     x     Δtx  is also related to the offset between the frequency-encoding gradient and acquisition window, but leads to a distortion and deformation of the object shape. This effect is coupled to
 
             e     -       Δ   ⁢           ⁢   t       T   2               
above. The term e jγBΔt  arises from demodulation and leads to a shift of the object within the field-of-view (FOV).
 
     In an embodiment, the offsets are calculated from a slope of a phase profile of at least one navigator echo. 
     At operation  1006 , the controller is also configured to apply the plurality of offsets to a k-space of the plurality of signals. 
     In an example embodiment, the systems and methods herein may provide for using the clock synchronization methods used in wireless communication systems with microsecond level accuracy may provide a useful solution here. Also, RF pulses can be used as clock sync signals without incorporating additional hardware into the setup schemes. 
     In an example embodiment, the systems and methods herein may provide for using highly stable accurate clock source (TCXO/OCXO) yielding around 100 ppb stability in the wireless RF coil. 
     In an example embodiment, the systems and methods herein may provide for estimators that can be substituted with other estimation techniques, e.g. Maximum Likelihood Estimators based on different noise models. 
     An alternative image post-processing approach involves utilizing a self-navigated technique where no additional data is acquired but correlations between successive k-space lines are performed to determine linear phase shifts from line to line in k-space. 
     The proposed navigator echo-based correction is immediately applicable to any wireless RF coil setup where frequency offsets can exist between transmit and receive RF functions during an MRI scan. It offers a relatively straightforward retrospective solution and the corrections can be performed on board to output the error or artifact free image data. 
     One or more embodiments provide that navigator echoes are one of the most straightforward approaches from which the linear phase shifts in the form of displacements along x and y can be recovered. 
     Additionally, one or more embodiments of this disclosure recognize and take into account that motion degradation on MR images can be attributed to macroscopic motion that encompasses both physiologic motion from respiratory, cardiac pulsations, or peristalsis, and involuntary subject movement during the scan. The latter effects are the main source resulting in loss of image sharpness. The problem is only exacerbated when one needs to acquire high-resolution data (on the order of microns) where subject movement on the order of millimeters affects the high-resolution data. The many correction methods for rigid body motion rely on detection of the pose changes that need to be decoupled from the correction routine. 
     One or more embodiments of this disclosure provide a system of implementing a set of miniature MRI wireless coils that serve as motion trackers for a prospective motion detection. Additionally, novel pulse sequences and motion correction algorithms also serve as features of this invention. The RF coils would function as additional set of coils (apart from the main imaging receive coils) solely for the purpose of motion detection by Faraday&#39;s principle of induction. 
     One or more embodiments of this disclosure provide smaller motion tracking wireless coils that will be positioned closer to the tissue or anatomical region being scanned thereby providing more accurate motion degradation information in the course of a routine scan. Additionally, FID navigator based pulse sequences will be incorporated for motion detection. In this prospective approach, motion-degraded data or lines of k-space can be reacquired, as real-time FID data acquired as part of the main scan can alert the user to ongoing subject-induced motion. 
     One or more embodiments of this disclosure provide that by positioning the wireless miniature RF coils closer to the subject (rather than on an accessory for a specific anatomical region), motion degraded data can be picked up more accurately from several distinct anatomical locations undergoing MR scanning. Also, the FID navigator approach has the potential to rapidly detect corrupted data points and reacquire them before the entire main scan is completed. 
     Wireless RF coils, either as a single loop coil or solenoid, can be integrated into a primary wired or wireless RF receive (Rx) coil setup to enable prospective motion detection and correction. They can be referred to “RF motion taggers”. A few of these coils are strategically placed on the subject near the Rx coil arrays. Their signal is linked wirelessly to the receive array by Faraday&#39;s law of mutual induction (inductive coupling (magnetic flux, dΦ/dt)). During the signal reception, the wireless RF motion taggers pick up signal in the vicinity. This signal generates a current dI/dt in the tagger and an associated magnetic field and flux as it passes through the imaging coil. The flux induces a voltage, V in the main RF coil that gets routed to the standard receiver. 
     One or more embodiments of this disclosure provide that novel pulse sequences based on a navigator approach can be used to prospectively update the orientation and position of the imaging volume so that it follows the patient or identifies motion-degraded portions of the data during the course of the acquisition and removes those data prior to image reconstruction or reacquires only that part which is degraded. 
     Rigid body motion can be monitored by changes in the free induction decay or FID signal over time in coil arrays. FID signals from local coil elements change as a function of object distance. The local coil sensitivities are being used from multi-channel coils to detect motion displacements during the course of the scan. If the object is sufficiently covered with the coil elements, the inverse problem of back-calculation of the rigid body motion parameters is then solvable. 
     For the FID navigators, in terms of the signal combination steps to detect motion and how much of it occurred, in a given pulse sequence such as the magnetization prepared rapid gradient echo (MP-RAGE), the first three repetition times (TRs) can be skipped since the longitudinal magnetization is building up there. Reference values (one per coil) may also be calculated. In equation 11 below, “t” is the repetition number, N, number of coil elements, and nav i (t) is the complex navigator data of coil element I in repetition number t. The number of incoming navigators is dependent on the number of coil elements for signal reception. For the implementation in one or more embodiments of this disclosure, the number of incoming navigators could be as low as three. Percental complex magnitude of the navigator signal could be calculated. It can yield a single value that can now be tracked over time. 
     
       
         
           
             
               
                 
                   
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                       t 
                       ) 
                     
                   
                   = 
                   
                     
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                           1 
                         
                         N 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                            
                           
                             
                               
                                 nav 
                                 i 
                               
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                             - 
                             
                               ref 
                               i 
                             
                           
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                             ref 
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                            
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
       FIG. 11  illustrates a motion detection process  1100  in accordance with an embodiment of this disclosure. A cause of motion degradation is involuntary subject motion that leads to either a linear phase shift of the k-space views or lines for translational motion or a rotation of the same k-space lines in the case of rotational motion. Both types of motion degradations can result in blurring and loss of sharpness in the image domain. The controller here may represent the processing device  210  and the memory element may be the memory  230  in  FIG. 2 . The embodiment of the process  1100  shown in  FIG. 11  is for illustration only. Other embodiments of the process  1100  could be used without departing from the scope of this disclosure. 
     At operation  1102 , the controller is configured to start an adaptive threshold process to determine motion degraded data. In an example, operation  1102  is performed by evaluating the incoming navigator point history, a collection of FID navigator signals or data points acquired per repetition time (TR). At operation  1104 , the controller is configured to the compare incoming FID navigator data points, Δ(n), to preceding points that are part of the regression time course for a given time period or TR. The regression time course is a plot of the navigator data points that is updated in real-time with each incoming signal or data point. 
     At operation  1106 , the controller is configured to evaluate incoming data points to see if they exceed the threshold of 3*std. deviation (TH) of all points in the regression time course. In an example embodiment, the controller may also be configured to determine the threshold and isolate that from other effects such as heating that may occur due to lengthy scans. Also, frequency shifts can be addressed that can cause drifts and changes in signals over time. A nominal threshold of three standard deviations of the points can be assigned (implying that it is outside a 99.7% confidence interval for a normal distribution). A more relaxed threshold entailing higher number of standard deviations, such as, for example but not limited to, 4*std. deviations or more can be used based on the imaging application being performed. 
     At operation  1108 , the controller is configured to determine whether the incoming data points are greater than the threshold. If not, at operation  1110 , the controller is configured to continue feeding data points into the navigator history for subsequent comparisons to the regression time course and for updating the adaptive threshold process. If equal or above the threshold, at operation  1112 , the controller is configured to label the TR or k-space line as motion-corrupted. 
     If above the threshold, at operation  1114 , the controller is configured to initiate a motion correction method or discard and repeat the same TR at the end of the scan. A corrupted k-space line or set of corrupted lines can be re-acquired at the end of the scan. In this example, the basic assumption is that subject may have moved the anatomy of interest being scanned back to the original position where it was at the start of the scan. 
     Other techniques such as floating navigators and self-navigated techniques can also be investigated and potentially be incorporated with this standalone hardware solution based on miniature RF taggers for motion detection and correction. 
     The embodiments of this disclosure are not relegated to a certain anatomical location and can be applied to any anatomical region with any type of primary RF coil (wired or wireless) for motion tracking. 
     Although the present disclosure has been described with an exemplary embodiment, various changes and modifications may be suggested to one skilled in the art. It is intended that the present disclosure encompass such changes and modifications as fall within the scope of the appended claims.