# Patent

## Title
Frequency swept excitation for magnetic resonance

## Abstract

A method of magnetic resonance is provided that uses a frequency swept excitation wherein the acquired signal is a time domain signal is provided. In one embodiment, the method comprises, applying a sweeping frequency excitation and acquiring a time domain signal. The sweeping frequency excitation has a duration and is configured to sequentially excite isochromats having different resonant frequencies. Acquisition of the time domain signal is done during the duration of the sweeping frequency excitation. The time domain signal is based on evolution of the isochromats.

## Background
CROSS-REFERENCE TO RELATED APPLICATION(S)
This application is a Continuation-In-Part of U.S. patent application Ser. No. 11/548,664, filed Oct. 11, 2006, entitled “Frequency Swept Excitation for Magnetic Resonance”, and also claims benefit under 35 U.S.C. § 119(e) to U.S. Provisional Patent Application Ser. No. 60/725,361, filed Oct. 11, 2005, entitled “Frequency Swept Excitation for Magnetic Resonance Imaging”, the content of which is incorporated herein in their entirety for all purposes.


GOVERNMENT FUNDING
This invention was made with Government support under Grant No. RR008079 awarded by the National Institutes of Health. The government has certain rights in this invention.


FIELD
A method of magnetic resonance is provided. More specifically, a method of magnetic resonance that uses a frequency swept excitation wherein the acquired signal is a time domain signal is provided.
BACKGROUND
Magnetic resonance techniques are applied in nuclear magnetic resonance (NMR) experiments and magnetic resonance imaging (MRI). In magnetic resonance techniques, the response of nuclear spins in a magnetic field is observed following excitation by a radio frequency (RF) field. There are three basic types of the RF excitation: sequential, simultaneous and random. Currently available techniques for both NMR and MRI using these types of RF excitation have limitations.
Several different NMR techniques have been developed including: continuous wave (CW), pulsed, stochastic, and rapid scan correlation spectroscopy.
Using CW techniques, an RF sweep is run exciting different resonating frequencies as a function of time. Typically the sweep has a low RF amplitude requirement. The CW sweep is run very slowly to maintain a steady state and avoid saturation of the signal. Thus, a large RF pulse will saturate the system and cannot be used. If the continuous wave sweep is run at a faster speed, “wiggles” will appear in the acquired signal. The resulting signal (or acquired signal) is looked at as a function of frequency. Historically, the first high resolution spectra of liquid samples were acquired using the CW technique. NMR spectroscopy using the CW technique became an important tool in the field of chemistry until the early 1970's. However, due to the slow rate of acquisition, CW NMR is time consuming and thus impractical for in vivo or clinical applications.
Pulsed Fourier Transform (FT) spectroscopy achieves efficiency and sensitivity beyond that of the CW technique. Using pulsed Fourier spectroscopy, a short, intense pulse at a constant frequency is applied that excites a plurality of resonances simultaneously. Typically, the pulse is a high power monochromatic RF pulse and there is a limited range of excitation frequencies. The resulting signal (or acquired signal) is looked at as a function of time. In the pulsed FT technique, the excitation pulse is generally assumed to be short (a delta function), so that the FT of this input function can be considered approximately equal to unity, and thus, the system spectrum (H(ω)) can be obtained directly via FT of the impulse response (h(t)). FT spectroscopy can achieve high sensitivity because, during a given sampling time, a pulse may be repeated multiple times and the noise averaged. FT spectroscopy further has good flexibility insofar as the spin dynamic may be managed using a variety of different pulses.
Stochastic NMR uses a long series of small flip angle RF pulses whose phase or amplitude is modulated in a random manner. The spin system generally remains in the linear region. The technique typically involves several hundred pulses with a pseudo randomly determined phase. Phase is generally determined by Maximal Length Binary Sequence (MLBS). MLBS approximates white noise. Stochastic NMR has a broader range of excitation frequencies than does conventional FT pulsed NMR. Systematic noise inherent in images obtained with random noise excitation is eliminated by using pseudorandom noise together with Hadamard transformation for data evaluation. A backprojection algorithm is used to reconstruct the images. A limitation in stochastic NMR is the need to create truly random excitation in order to avoid systematic noise artifacts. During excitation, a flip angle is used to define the angle of excitation for a field echo pulse sequence. The flip angle is the angle to which the net magnetization is rotated or tipped relative to the main magnetic field direction via the application of an RF excitation pulse at the Larmor frequency. The small flip angle used in stochastic NMR contributes to low sensitivity of the system. The acquired signal typically has a low amplitude. Further, hardware limitations frequently limit the utility of the system.
Rapid scan correlation spectroscopy combines the rapidity of FT NMR with the dynamic range of CW NMR. Rapid scan correlation spectroscopy uses a series of chirp pulses. The chirp pulses and the acquired pulses are correlated to produce a spectra. While rapid scan correlation spectroscopy is faster than CW NMR, its slow speed remains a limitation in its application.
In the evolution of high resolution NMR, pulsed Fourier NMR spectroscopy has continued to dominate the field, while the CW NMR technique essentially became obsolete and was used only for niche applications.
The above discussion relates specifically to high resolution NMR, typically performed in a laboratory setting on sample objects generally of test tube size. Another field of application for magnetic resonance techniques is clinical applications, in vivo applications, or MRI applications. MRI has technical requirements beyond those of NMR. Because the objects of interest (such as the brain or breast) is usually much larger than a test tube, the static and RF fields used in MRI are more inhomogeneous than those used in high resolution NMR. For applications on living systems, the need to avoid tissue heating places limits on the intensity and duty cycle of the RF irradiation that can be safely used, also known as the specific absorption rate (SAR) limitations. Similarly, when used in vivo, the subject must remain generally stationary during the MRI. Thus, slow techniques are difficult in clinical applications.
Several MRI techniques have been developed including CW MRI, pulsed FT MRI, including Ultra-short Echo Time (UTE) MRI, and stochastic MRI. Additionally, rapid scan techniques have been considered for imaging using electron paramagnetic resonance (ER).
Continuous wave MRI system using low RF power has been applied to study a variety of heterogeneous materials exhibiting very short relaxation values. As with CW NMR, CW MRI must be run at a very slow rate. This rate typically precludes application in clinical applications.
Pulsed FT MRI is useful in imaging of soft tissue but has limitations in the imaging of materials having fast relaxing spins (including semi-solid objects such as bone). These techniques use a short monochromatic RF pulse for excitation, followed immediately by signal acquisition, all performed in the presence of a field gradient. In MRI applications, the RF pulse can approach a delta function only by restricting the flip angle to <<90°. As the pulse length increases, the pulsed FT spectrum suffers from increasing phase and baseline distortions. Further, although these fast imaging sequences have minimal demands on gradient hardware performance, they are severely limited by the length of the pulse. To achieve broadband excitation with limited ω1 amplitude, a small flip angle is employed, which results in low S/N. Specifically, the width of the pulse leads to low sensitivity and low contrast in clinical applications. Artifacts such as increasing phase and baseline distortions can be avoided by replacing the free induction decay (FID) with an echo acquisition. Echo time is the time between the application of a pulse and the peak of the echo signal in spin-echo sequences. However, the finite echo time used to form an echo leads to reduced sensitivity to fast relaxing spins and increased susceptibility to motion and flow artifacts. For imaging of objects having fast relaxing spins, the echo time must be short. Pulsed FT MRI typically has a relatively long echo time.
One of pulsed FT MRI methods, Ultrashort Echo Time (UTE), was developed to image fast relaxing spins using FID acquisition. The UTE sequence employs a self refocused excitation pulse, followed immediately by a pulsed-on gradient and signal acquisition. UTE MRI has short “echo” times, which is good for imaging of fast relaxing spins. However, UTE pulse sequences use a growing gradient and simultaneous acquisition. The gradient slew rate is the rate of ascent or descent of a gradient from zero to its maximum amplitude, either positive or negative. The shorter the rise time, the faster the gradients and smaller echo time. As a result, UTE has better sensitivity to fast relaxing spins. Thus, it is generally desirable that the gradient have a fast slope. Using UTE MRI, there is a gradient limitation that limits the resolution of the images. The minimum duration needed to execute the excitation pulse and gradient switching are limited by the available RF amplitude and the gradient slew rate, respectively.
As discussed with respect to stochastic NMR, stochastic MRI has a small flip angle and thus has low sensitivity and low contrast in imaging.
While not currently implemented in MRI, rapid scan techniques have been used in electron paramagnetic resonance (EPR). These techniques have generally been considered unsuitable for MRI because of the following difficulties. Rapid scan utilizes a fast gradient echo sequence such as a series of chirp pulses. To avoid non-uniform weighting of the spectrum, the excitation frequency must be swept linearly (chirp pulse), which excludes the use of tailored frequency sweeps. Generally, an excitation profile in MRI applications must be rectangular. This is not readily achievable using short chip pulses and, thus, a rapid scan MRI using such chirp pulses would result in a relatively bad excitation profile. In rapid-scan FT techniques, the detector frequency is synchronous with the time-dependent transmitter frequency, and thus, correlation must be used to restore the undistorted absorption line by removing the “ringing” that persists following passage through resonance. In accordance with the Nyquist theorem, sampling in the frequency versus time domain places an upper limit on the sweep rate. Thus, rapid scan FT MRI, even if suitable for implementation, has an inherent speed limitation and its slowness limits use in clinical applications.
Using available techniques, it is difficult to image objects having a broad distribution of relaxation times, including very short spin-spin relaxation times, such as semi-solid objects including bone, macromolecules, and quadripolar nuclei. Accordingly, it would be desirable to have a technique to image materials having short spin-spin relaxation times that is sufficiently fast for in vivo application.
SUMMARY
A method of magnetic resonance is provided that uses a frequency swept excitation wherein the acquired signal is a time domain signal is provided.
In one embodiment, the method comprises, applying a sweeping frequency excitation, acquiring a time domain signal, and achieving a steady, oscillating, or pseudo-steady state. The sweeping frequency excitation has a duration and is configured to sequentially excite isochromats having different resonant frequencies. Acquisition of the time domain signal is done during the duration of the sweeping frequency excitation. The time domain signal is based on evolution of the isochromats.
In another embodiment, the method comprises exciting a specimen with a sweeping frequency excitation, applying at least one functional pulse, acquiring a time domain signal from the specimen, and processing the acquired time domain signal. The frequency excitation has a plurality of alternating excitation segments and quiescent segments. The excitation segments are modulated according to at least one of a phase modulation function and a frequency modulation function. The acquired time domain signal is based on resonance during a plurality of the quiescent segments.
While multiple embodiments are disclosed, still other embodiments of the present invention will become apparent to those skilled in the art from the following detailed description. As will be apparent, the method disclosed herein is capable of modifications in various obvious aspects, all without departing from the spirit and scope of the present techniques. Accordingly, the detailed description is to be regarded as illustrative in nature and not restrictive.



BRIEF DESCRIPTION OF THE FIGURES
FIG. 1 illustrates a frequency swept excitation method in accordance with one embodiment
FIG. 2 illustrates a pulse sequence scheme in accordance with one embodiment.
FIG. 3 illustrates simulation results in the phase-modulated and frequency-modulated rotating frames, and the magnitude, of a single isochromat, using a frequency-swept excitation in accordance with one embodiment.
FIG. 4A illustrates correlation processing in accordance with one embodiment.
FIG. 4B illustrates convolution processing in accordance with one embodiment.
FIG. 5 illustrates real parts of a response and RF pulse spectrum and real and imaginary parts of a system spectrum in accordance with one embodiment.
FIG. 6 illustrates simulated excitation performance of a pulse in the intermediate passage region in accordance with one embodiment.
FIG. 7 illustrates images of slices of a 3D image of a thermoplastic object taken with the frequency swept method in accordance with one embodiment.
FIG. 8 illustrates comparative images of a specimen of bovine tibia images using a 2D gradient echo image and using the frequency swept method in accordance with one embodiment.
FIG. 9 illustrates images of a tooth taken using the frequency swept method in accordance with one embodiment.



DETAILED DESCRIPTION
A method of magnetic resonance is provided that uses a frequency swept excitation wherein the acquired signal is a time domain signal. The method may be referred to as a frequency swept excitation method and has applications in a plurality of fields including, but not limited to, human and animal medicine, dentistry, material science, security, and industry. The frequency swept excitation method may be used in nuclear magnetic resonance spectroscopy, magnetic resonance imaging, electron paramagnetic resonance (EPR), nuclear quadrupole resonance (NQR), and others. The frequency swept excitation method may be used in studies of fast relaxing spins as well as magnetic resonance imaging using non-uniform (inhomogeneous) magnets or in imaging of inhomogeneous fields.
Using the frequency swept excitation method, excitation of nuclear spins is achieved using a radio frequency sweep. In one embodiment, the excitation comprises a series of pulses, each pulse having an excitation segment and a quiescent segment. The frequency or phase is swept within each pulse. A signal is acquired as a time domain signal during the quiescent segment. Acquiring the signal during the quiescent segment, and thus during a portion of the excitation pulse, may be referred to as acquiring in a time-shared manner. The acquired signal is treated as a signal that varies as a function of time and is looked at in the time domain. After signal acquisition, the signal is processed, for example using a correlation method or a convolution, to correct the acquired signal by separating the spin system spectrum. The processed signal can then be used in imaging. Generally, the method affords fast and quiet magnetic resonance imaging. Standard MRI scanners may be programmed to use the frequency swept excitation technique.
In one embodiment, the frequency swept excitation method uses time shared acquisition by incorporating an excitation segment and a quiescent segment during the RF sweep such that excitation and acquisition are nearly simultaneous. In another embodiment, the frequency swept excitation method performs excitation and acquisition simultaneously, for example by decoupling the transceiver and transmitter. Either of the time-shared or simultaneous embodiments of the frequency swept excitation method may be used for imaging objects having a broad distribution of relaxation times, including very short spin-spin (or transverse or T2) relaxation times. In some embodiments, the frequency swept method is sensitive to all excited spins having spin-spin relaxation time larger than the reciprocal value of the spectral width (thus, T2>2π/sw). Using conventional MRI techniques, excitation and acquisition events are separated by the length of time known as the echo time (TE), which is typically >1 ms. This length of time is generally too long to allow detection of slowly tumbling nuclei with short spin-spin relaxation time (T2). Accordingly, using conventional MRI techniques, it is difficult to image objects having short spin-spin relaxation times.
The present method has a near zero echo time (or TE approaching 0) because signal acquisition can begin within a few microseconds after excitation. Alternatively, the method may have a zero echo time where signal acquisition occurs during excitation. Because the frequency swept method has a zero or near zero “echo time,” it is generally less sensitive to motion and flow artifacts than conventional magnetic resonance methods. Thus, the frequency swept method has a reduced signal loss due to either diffusion in the presence of a gradient or uncompensated motion as compared with other magnetic resonance methods. The frequency swept excitation method may be beneficial for studying objects having very fast spin-spin relaxation rates such as macromolecules, semi-solids, and quadrupolar nuclei. Examples of quadrupolar nuclei that may be imaged include sodium-23 MRI, potassium-39, and boron-11. The present method is further insensitive to field inhomogeneity and thus can be used, for example, in imaging tissues near metal objects such as metal implants. Further, the method may be used in magnetic resonance imaging and spectroscopy using non-uniform (inhomogeneous) magnets (for example, having inhomogeneous main magnetic field or RF field).
In various embodiments, frequency swept pulses improve signal-to-noise (SNR) ratios, suppress artifacts, improve experimental accuracy, and reduce peak RF power. The frequency swept method generally is relatively quick because it avoids delays associated with refocusing pulses or gradient inversion and combines the time used for excitation with the time used for acquisition. Because different frequencies may be excited sequentially the resulting signal is distributed in time, leading to a decreased amplitude of the acquired signal. This allows more effective utilization of the dynamic range of a digitizer. Further, because the frequency swept method may use a small step when changing gradients between projections, the fast gradient switching of conventional magnetic resonance techniques that creates loud noise can be avoided. This property can be important for MRI scanning of the patients having ligyrophobia.
As shown in FIG. 1, in accordance with one embodiment, the frequency swept excitation method 10 excites 12 nuclear spins using a frequency sweep. In one embodiment, the sweep comprises a series of pulses, each pulse having excitation segments and quiescent segments. After excitation, an acquisition signal is acquired 14 from which an image may ultimately be produced. The acquisition signal is acquired as a time domain signal. In one embodiment, signal acquisition is done during the quiescent segments of each pulse. After signal acquisition, the signal is processed 16 to extract the useful signal from the acquired signal system response. Processing, also referred to as post processing, may be done, for example, by correlation or convolution. Using the frequency swept method, the spin response to the swept RF excitation behaves effectively as a linear system for flip angles up to 90°. Hence, the frequency swept method affords high S/N without observable image artifacts from violating the linearity condition.
For imaging, a steady state may be established. Generally, a steady state is a state of spins which leads to an equilibrium magnetization for the longitudinal and transverse magnetization, or, when the magnetization at or after each pulse is the same as the previous pulse. As may be appreciated, with the driving of T1 (spin lattice relaxation time) and magnetization of decay of T2 (spin-spin relaxation time), a steady state may not always be inherently achieved. More specifically, a non-zero steady state can develop for both components of magnetization (transverse and longitudinal). Further, because the frequency sweep is done during a gradient, achievement of a steady state may present challenges. Accordingly, various techniques for achieving a steady state are provided herein. In some embodiments, these methods apply to the excitation portion of the method. In other embodiments, these methods apply to the processing portion of the method. Thus, steady state may be achieved during excitation and acquisition or may be done at the beginning of imaging.
To use the frequency swept method for NMR measurements, the signal is recorded, and to perform MRI, a procedure is implemented to encode spatial information. Ways to accomplish this are described herein. As described, each pulse of a series of pulses is divided into a plurality of segments (e.g., 512) separated by short delays (e.g., 10 μs each), and during each of these short delays, an analog-to-digital converter (ADC) samples one or more points. These short delays used for signal recording have no or minimal effect on pulse performance or the steady state.
Excitation
As shown in FIG. 1, nuclear spins in the object of interest are excited 12 using a frequency sweep. The frequency sweep may comprise a series of frequency modulated pulses, also referred to as a series of frequency-swept pulses,. In one embodiment, the frequency excitation is non-random but may not be continuous or linear. The pulses may be generated in any suitable manner, for example using a transmitter as is known in the art. The frequency-swept pulses sequentially excite isochromats over each pulse, and as a result, the phase of the magnetization varies in a quadratic manner along the readout direction. In accordance with one embodiment, the frequency of the RF irradiation used to excite signals is modulated in time during each pulse. In accordance with another embodiment, the phase of the RF irradiation used to excite signals is modulated in time during each pulse. Thus, the signals are continually out of phase. The frequency-swept excitation distributes the signal energy in time. Dynamic range requirements for proper signal digitization and peak RF power requirements are thereby reduced compared with conventional MRI.
While discussion is made of sweeping the frequency during each pulse, such sweeping may alternatively be done by sweeping the phase during each pulse. Thus, the pulses may alternatively be referred to as phase-swept or phase modulated.
An example pulse sequence scheme 20 is illustrated in FIG. 2. In the embodiment of FIG. 2, the pulse sequence comprises a series of pulses, each pulse comprising excitation segments and quiescent segments. In alternative embodiments, the transmitter and receiver may be decoupled and quiescent segments may not be used. In one embodiment, the pulse sequence is delivered while a gradient is applied, as discussed with respect to signal acquisition. The gradient magnetic field can be used to alter (collectively and sequentially) the influence of the static magnetic field B0 on the imaged object by increasing or decreasing the field strength.
FIG. 2 illustrates the pulse sequence scheme 20, a presentation of the repeated part of the sequence 22, and a magnified view of the pulse segments 24. The scheme 20 employs a sequence of RF pulses (for example, p pulses wherein p represents the number of pulses), each having a duration Tp. In one embodiment, Tp is in the millisecond range. Each pulse is divided into N segments, each having RF power on for duration τp following a delay with RF power off. Thus, each pulse comprises an excitation segment and a quiescent segment. Thus, as shown in the repeated part of the sequence 22, the scheme employs p frequency-modulated pulses with a short repetition time Tr that exceeds the pulse length Tp. In one embodiment, the repetition time Tr exceeds the pulse length Tp by at least the amount of time needed for setting a new value (or orientation) of a magnetic field gradient used to encode spatial information for signal acquisition. The images may be processed using a 3D back-projection reconstruction or using gridding with reconstruction, although other acquisition and reconstruction methods are possible.
The RF pulses may be of the family of hyperbolic secant (HSn) pulses which utilizes both amplitude and frequency modulation. As will be discussed more fully below, in some embodiments, the RF pulses are run at a linear or subadiabatic range. A transition may be made from the adiabatic to the linear region by reducing the RF amplitude or increasing the sweep rate, while other pulse parameters remain constant. The amplitude (ω1(t)) of the pulse may be written as:

ω1(t)=γB1(t),  (1)

(in units of rad/s) where γ is the gyromagnetic ratio and B1(t) is the time-dependent amplitude of the RF field. The time dependency of amplitude (ω1(t)) and phase (ωRF(t)) of HSn pulses can thus be written as,





  
    
      
        
          
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where ω1max is the maximum pulse amplitude, ωc is the carrier frequency (usually the center frequency in the sweep range), Bωis the total bandwidth of the frequency sweep, Tp is pulse length, β is a dimensionless truncation factor (sech (β)=0.01), and C is a normalization factor given by





  
    
      
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As shown at 20 of FIG. 2, the frequency swept pulse is represented as a histogram of N different pulse elements with amplitudes ω1(t) and offset frequencies ωRF(t)−ωc. The excitation bandwidth is not constrained by the amplitude of ω1. Delays τa a are inserted into the pulse pattern after each pulse element of duration τp, making a dwell time dw=τp+τa. The receiver is blanked during τp and open during τa for data sampling. Data sampling, discussed below, is performed during τa, shown in the magnified view of the pulse segments 24. The introduction of delays into the pulse shape leads to a basically unmodified excitation profile.
The frequency sweep may be done while a gradient is applied. Such gradient may be constant or may be shaped. Shaped gradients may be useful in straightening projections and thus may have particular application in an inhomogeneous field, the gradient field compensating part or all of the inhomogeneity field. Further, when field inhomogeneity is a factor, a gradient shape and frequency sweep may be calculated to obtain a desired projection angle trajectory or plane, the projection being determined by the sum of the gradient and inhomogeneity fields.
Generally, the frequency sweep excites the object of interest in a time sequential manner along the direction of the gradient. In some embodiments, the frequency sweep may be timed to coincide with a motion of interest, such as flow or other physiological precesses, such that the excitation follows and overlaps with the moving object. Depending on the implementation, timing the frequency sweep to coincide with the motion of interest may cause enhanced or decreased MR signal. This further reduces motion artifacts that can result in the acquired signal.
In imaging of subjects comprising fat and water, artifacts can develop. Such artifacts may be termed chemical shift artifacts, black boundary artifacts, spatial misregistration artifacts, or relief artifacts. Generally, during frequency encoding, fast protons precess differently from water protons in the same slice because of their magnetic shielding. Because of the difference in resonance frequency between water and fat, protons at the same location are misregistered (dislocated) by the Fourier transformation when converting MRI signals from frequency to spatial domain. Where fat and water are in the same location, as is commonly the case in tissue, this artifact can be seen as a bright or dark band at the edge of the anatomy. Some embodiments of the present method reduce or remove such artifacts. In one embodiment, two frequency sweeps are run, the sweeps being run in the opposite direction. In another embodiment, two frequency sweeps are run, the sweeps being run in the same direction, but the gradient being reversed for each sweep. In yet another embodiment, two to four frequency sweeps are run, the sweeps being run in opposite directions and the gradients being reversed between sweeps. Thus, the present method provides a method of separating fat and water signals using a frequency swept pulse and reversing the direction of the frequency sweep and/or changing the sign of the gradient. Additional post processing, described below, may be used to improve image quality and reduce water in fat/water separations. While this is described specifically with respect to reducing chemical artifacts between fat and water, it may be used for reducing chemical artifacts between two or more other components.
Excitation hardware imperfection can result in systemic noise in resulting spectra for images. Because the frequency of these noises does not depend on an excitation frequency, correction may be done in the frequency domain. For example, artifacts, such as image artifacts or spectroscopy artifacts, may be removed by randomly or pseudo-randomly varying the carrier frequency from one frequency sweep to the next. This may be termed “jittering” the carrier frequency. Generally, a jitter is a variation of one or more signal characteristics, such as the interval between successive pulses, the amplitude of successive cycles, or the frequency or phase of successive cycles. Thus, jitter can apply to a number of signal qualities (e.g., amplitude, phase, pulse width, or pulse position). In one embodiment, the frequency is jittered. This may comprise jittering of the excitation frequency and/or jittering of the acquisition frequency. If jittering is employed, it may be desirable to “unjitter” the acquired signal. This may be done during excitation and acquisition or in post processing. Generally, if both the excitation frequency and the acquisition frequency are jittered, unjittering is done during excitation and acquisition. If only one of the excitation frequency or the acquisition frequency is jittered, unjittering may be done during post processing. Jittering of the carrier frequency can be done to shift the resulting spectre in an inverse direction before image reconstruction.
Returning to the excitation pulses, the relationship between the continuous HSn pulse and its time-shared variant (shown) is analogous to the relationship between a long pulse of constant amplitude and a DANTE pulse train which closely approximates the excitation profile of the continuous pulse, but produces excitation sidebands at multiples of the pulse repetition rate. Because the repetition rate of the pulse elements and the acquisition rate may be equal to the inverse dwell time, the first excitation sideband is generally set outside of the acquisition spectral window. The offset frequencies may be created by incrementing the phases of pulse elements. In this case the maximum reachable excitation bandwidth according to the Nyquist theorem is approximately equal to the acquisition spectral width (sω):




  
    
      
        
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            2
            ⁢
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when the maximum phase increments (in this case, at the beginning and end of the pulse) are equal to π. By proportionally decreasing the phase increments, only a portion of spectral window may be excited.

One can assume that the RF field excites each isochromat instantaneously when its resonance frequency is attained in the frequency sweep. FIG. 3 illustrates the oscillatory motion 30 of the magnetization components of a given isochromat having frequency ω. The isochromat excitation time in FIG. 3 is shown by the vertical dotted line 32. In FIG. 3, MxPM(t) 34 presents the x-axis component of the transverse magnetization vector of the isochromat in a reference frame known as the phase-modulated (PM) frame, which rotates around the static magnetic field direction (z) with an angular velocity ωc equal to the center frequency in the sweep range. MxFM(t) 36 is the x-axis component in a frequency-modulated (FM) frame, which rotates synchronously with the (time-dependent) pulse frequency ωRF(t). FIG. 3 also shows the absolute value of the transverse magnetization




  
    
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  38.




Similar oscillatory behavior may arise in the rapidpassage, linear region, which satisfies the conditions

αT22>>1  (6a)

and

α/ω12>>1,  (6b)

where αis the sweep rate; in this example α≈Bw/2πTp. As may be appreciated, a difference arises between the rapid passage, linear region and the rapid passage, adiabatic region, wherein the latter condition is α/ω12<<1. Accordingly, the transition from the adiabatic to the linear region requires reducing the RF amplitude or increasing the sweep rate, while other pulse parameters remain constant. In this way, an adiabatic passage pulse, such as a HSn pulse, can be used in the rapid passage, linear region to rotate the magnetization by an angle <90°. Below, all presented simulated and experimental data were generated using excitation in the rapid passage, linear region.

The frequency swept excitation method sequence has less stringent constraints than indicated by Eqs. (6a) and (6b). First, because the pulse is segmented, the average value of ω1(t) scales inversely with τp/dw. Second, the correlation method, described below, works well up to a rotation angle near 90° before significantly violating the linearity condition of Eq. (6b). The frequency swept excitation method is not restricted to the rapidpassage region by Eq. (6a). For example, the frequency swept excitation method may also be used in the intermediate passage, linear region, with the consequences of sacrificing signal-to-noise ratio (S/N) and resolution.
FIG. 3 illustrates that the isochromat begins its motion slightly before resonance is reached and thereafter decays. The wiggles before the excitation time observed in PM frame fully disappear in FM frame. Thus, the wiggles are not a function of the resonance frequencies of the isochromats and instead depend only on the frequency-modulated function ωRF(t). In another words, until the moment resonance is attained, the isochromat follows the effective RF field vector to the transverse plane. At the time of resonance, the isochromat is released from the RF pulse's influence and has an almost free precession with a small decaying modulation which can be seen in magnitude mode (part c of FIG. 2) as wiggles after the resonance time. Because these wiggles have a variable frequency, after Fourier transformation (during processing, described below) their contribution is spread across the resulting spectrum. The spectral contamination arising from wiggles of different isochromats are additive and thus are more prominent when imaging is performed on an ensemble of isochromats.
In some embodiments, first and second sequences may be run wherein gradient-, spin-, or simulated echoes are created in at least one of the sequences. This can be used to filter spin-spin relaxation times (T2). Using a gradient echo, an echo is produced by reversing the direction of the magnetic field example. Thus, for example, a first acquisition is performed using a first gradient and applying a pulse (or pulse sequence) and a second acquisition is performed using a second gradient (opposite the first gradient) without applying a pulse. Using a spin echo, a first acquisition is performed using a first gradient and applying a pulse (or pulse sequence) and a second acquisition is performed using the first gradient without applying a pulse. Using a stimulated echo (a form of spin echo), a first acquisition is performed using a first gradient and applying a pulse (or pulse sequence) wherein the pulses are typically 90° pulses and a second acquisition is performed using the first gradient without applying a pulse. As will be described with respect to post processing, the first and second acquisitions can be processed to remove data from the first acquisition.
In alternative embodiments, two more images may be compiled with or without weighting to enhance or suppress features in the image originating from T2 or T1 differences.
As previously discussed, in some embodiments, a steady state may be achieved during excitation and acquisition. Preparation pulses and gradients may be used to establish a steady or oscillating spatial magnetization state. More specifically, with respect to excitation, radio frequency pre-pulses, with or without gradient pulses, may be used to prepare the initial and steady state magnetization state, for example, to produce T1, T2, T1rho, T2rho, and blood flow contrast. In one embodiment, a subset of gradients, for example, skipping or decimating, is used during preparation pulses In another embodiment, constant or varying radio frequency power is used during the preparation pulses. Thus, the magnetization may be driven to a steady state using radiofrequency pre-pulses. In yet another embodiment, periodic reversal of gradients is used during the preparation pulses.
Thus, excitation may be preceded or followed by a pulse, for example a radio frequency pulse, for preparation, spoiling, or restoration of the magnetization. Such pulse may be referred to as a functional pulse. The functional pulse may be a frequency swept pulse. In various embodiments, the pulse may cause an inversion of the magnetization; excitation; saturation; partial, single, or multiple rotations of the magnetization around the B1 field; or others. A gradient may be applied prior, during, or after the pulse. When used as a preparation pulse, the effects of the preparation pulse may be localized in one or more spatial dimensions. Using the pulse, magnetization may be suppressed, saturated, spoiled, or enhanced according to T2, T2*, T1, T1rho, or T2rho. Using the pulse, magnetization may be suppressed, saturated, spoiled, or enhanced according to the diffusion of magnetization, the flow of magnetization, perfusion of a tissue, according to a chemical shift, or presence, absence or concentration of an endogeneous or externally applied, injected, or placed contrast agent. Magnetization may result from water, lipids, silicone, or other. Generally, any suitable pulse or gradient may inserted between the swept excitation and acquisition to prepare and maintain the spin system in a steady state otherwise not achievable, as well as to change or enhance contrast, suppress unwanted signals due to differences in T1, T2, T1rho, T2rho, chemical shift, and spatial location parallel or orthogonal to the projection direction.
Acquisition
As shown in FIG. 1, a time domain signal is acquired 14. Signal acquisition can be done nearly simultaneously with excitation. Specifically, signal acquisition may be done during quiescent segments of a pulse. In accordance with the Nyquist theorem, sampling in the frequency versus time domain places a lower limit on the sweep rate used the frequency swept method but places no upper limit on the sweep rate. The lack of an upper limit on the sweep rate is especially advantageous for MRI applications. In alternative embodiments, signal acquisition may be simultaneous with excitation. In various embodiments, a digital filter may be used during acquisition to exclude folding effect from the outside of field of view signal.
Signal acquisition may be done in any suitable manner, for example using a receiver to measure current, voltage, impedance, or other, as is know in the art. In one embodiment, the receiver is set to a constant frequency and thus the acquired signal behaves as MxPM, shown in FIG. 2, with the abscissa representing time (t). Following the excitation time (dotted line), the ensuing evolution resembles a FID. To obtain the spectrum, correlation, described below, may be used to remove the influence of the ωRF(t) function and to unscramble the phases of different isochromats having different excitation times.
As previously discussed and shown in FIG. 2, the frequency swept pulse is represented as a histogram of N different pulse elements with amplitudes ω1(t) and offset frequencies ωRF(t) −ωc. In one embodiment, delays τd are inserted into the pulse pattern after each pulse element of duration τp, making a dwell time dw=τp+τd. The receiver is blanked during τp and open during τd for data sampling. Thus, in one embodiment, acquisition (or data sampling) is performed during the delay τd (also referred to as a quiescent segment), after the pulse segment. More specifically, referring to FIG. 2, data sampling is performed at time τa shown in part c of Figure, using a time-shared method. Because excitation is temporarily suspended during the delay, acquisition may be performed without acquiring the RF pulse. Thus, the frequency sweep is broken into excitation segments and quiescent segments wherein acquisition is performed during the quiescent segments and, thus, during the frequency sweep. This is referred to as time-shared excitation and signal acquisition. In some embodiments, signal acquisition may start before the quiescent segment or extend beyond the quiescent segment. In alternative embodiments, acquisition may be performed simultaneously with excitation by decoupling the transmitter and transceiver, thereby avoiding acquisition of the RF pulse.
The time-shared excitation and signal acquisition maybe done in the presence of an applied magnetic field gradient. Magnetic field gradients are used to change the strength of the magnetic field B0 in a certain direction. The magnetic field gradient can be used to select a region for imaging and also to encode the location of MR signals received from an object being imaged. In one embodiment, the applied magnetic field gradient is: G=(G î+Gyĵ+Gz{circumflex over (k)}). The field gradient is used to impart on the spins a spatially dependent Larmor frequency ω(r)=γ(Gr+B0), where r is the coordinate vector and B0 is the static magnetic field. In one embodiment, the field gradient used for spatial-encoding is stepped in orientation in an incremental manner, which results in low acoustic noise—as opposed to techniques wherein the field gradient is pulsed on and off.
In one embodiment, the minimum temporal spacing of pulses, or repetition time (TR), is Tp plus the amount of time (tG) needed to make an incremental change in the orientation of G. After acquiring frequency-encoded projections, 3D images can be reconstructed, for example by using a 3D backprojection algorithm or gridding. In one embodiment, the minimum acquisition time required to obtain each projection is

At=tG+2πN/sw.  (7)

For example, with acquisition parameters that standard MRI scanners can readily achieve, sw/2π=100 kHz and tG;=0.3 ms, a 3D image with matrix size =128×128×128 can be acquired in less than 30 s. A further  ̃30% time reduction is possible without affecting image quality using an equidistant projection sampling method.

Acquisition of the signal resulting from the frequency swept pulse can be done in a manner to capture or freeze motion along the direction of the gradient. The object of interest is excited in a time sequential manner along the direction of the gradient. As the excitation signal sweeps across the object, motion is captured or frozen in acquisition
As previously discussed, to remove artifacts such as image artifacts or spectroscopy artifacts, the excitation frequency and/or the acquisition frequency may be jittered. Generally, if both the excitation frequency and the acquisition frequency are jittered, no further unjittering need be done. If only one of the excitation frequency or the acquisition frequency is jittered, unjittering may be done during post processing.
In one embodiment, acquisition is done radially. Every spectrum that is taken by applying a gradient gives one projection of the object: a projection of the object to gradient direction. To reconstruct an image of the object, the object is viewed from different angles. Thus, to create an image, it may be desirable to sample points along a predefined set of angles in a hemisphere or sphere. Generally, each point viewed may be equidistant from another point such that the sampling is isotropic. The more projections used, the more resolved resulting image is after reconstruction. That said, looking at an object from one direction (for example the Y direction) will give the same projection as looking at the image from the opposite direction (for example the −Y direction) with the projection being changed from left to right or right to left. Thus, a half circle (for a 2d image, angle=0-180) or a hemisphere (for a 3d image) can be used to construct an image; the other half circle or hemisphere will provide the same projection in the opposite direction. However, in some circumstances it may be desirable to take projections from each direction because taking images from each direction (for example, Y and 'Y) can give information about artifacts. However, while there may be some advantages to sampling the entire sphere (for example, to minimize artifacts through cancellation), sampling the entire sphere takes twice as much time as sampling a hemisphere. Thus, sampling a hemisphere and minimizing artifacts through processing and post processing may be done. In one embodiment, sampling is done radially along the hemisphere such that the view ordering is generally 2 or 3d radial ordering.
In taking projections, the object is imaged from different angles. For ease of explanation, a 2D image is referred to, however it is to be understood that this discussion applies equally to a 3D image. If an object is viewed along a half circle, the image is viewed from an angle of 0 to an angle of 180. In viewing the object, projections are taken at a plurality of angles from 0 to 180, inclusive. Thus, for example, the object may be viewed N times (for example, 181 times, starting at an angle of 0 and ending at an angle of 180), stepping the angle of the projection in 1 degree increments. When sampling is done in order along a stepped sequence, it may be referred to as sequential sampling. The order of taking the views is referred to as view ordering.
As described below, generating an image from a plurality of projections, each projection being separated by a small azimuthal separation (the separation between the angles sampled) can create noise. Thus, image reconstruction from a series of projections generally is undertaken under the influence of noise. To reduce the noise (SN) on a single projection, repeated acquisitions can be performed. Within a finite time period this forces a tradeoff between the number of different projections and the level of noise in each projection. Repeated acquisitions of a particular projection may be done by repeating the view of the entire object, thus, by running the projections again sequentially, or may be done by repeating, randomly or in a predetermined order, projections.
In some embodiments, viewing may be done randomly or pseudo-randomly and thus may be referred to as random view ordering. Thus, for example, the same N angles (for example, 181) may be viewed in a random order. Such random view ordering may be useful in image reconstruction to permit motion correction or to change steady state conditions and achieve different contrasts.
Random or pseudo-random view ordering may be used to permit motion correction. In some embodiments, radial acquisition comprises sampling along the sphere or hemisphere in the order of a radial line drawn through the sampling set, or sequentially as described above. Because all points in a region are sampled sequentially, if motion occurs during the sampling of those points, it may be difficult to correct the data to account for the motion because the motion will be reflected in all the sampled points in a given region. By using random or pseudo-random sampling, points in a region are sampled at different times. If a motion occurs, only some points in any given region will be effected by the motion. Thus, the data may be corrected by estimating the correct data point or by eliminating an aberrant data point.
Random or pseudo-random view ordering may further be used to change steady state conditions and achieve different contrasts. Excluding relaxation parameters of the system, the same N views sampled in a random order will give the same images. However, because there is relaxation, changing the view order, or using a random view ordering, the steady state condition is changed, which can result in different contrasts. The same N view we can get by changing angles in different way, let say randomly.
Further, in some embodiments, the entire hemisphere or half circle may not be sampled. For example, when preparation pulses, with or without gradient pulses are sued to achieve a steady state, a reduced number of angles may be sampled. For example, a partial subset of angles can be used that represents the end of a prior imaging trajectory.
Acquisition may further be done according to an asymmetric variation. Using an asymmetric variation, the cut off of the pulse is not the same on each side of the pulse. This acquisition after the pulse may be used for equalizing weighing of long T2 signals along the projections.
Post Processing
To extract useful information from the spin system response, post processing may done to correct the acquired signal. Thus, as shown in FIG. 1, the time domain signal may be processed 16. Post processing may be done, for example, using a correlation method or a convolution method. As will be described, correlation 40 comprises Fourier transforming the excitation signal and the acquired time domain signal and processing the FT signals in the frequency domain, shown in FIG. 4a. Deconvolution 50 comprises processing the excitation signal and the acquired time domain signal in the time domain and Fourier transforming the processed signals, shown in FIG. 4b. In some embodiments, the frequency swept excitation method may be operated in a rapid updated mode to reach high temporal resolution in dynamic studies. This pseudo-temporal resolution is possible because projection reconstruction, unlike phase encoded imaging, samples the center of k-space with every acquisition. This acquisition method is relatively insensitive to sample motion, which is advantageous for imaging live objects.
It is to be noted that the Fourier transformed projections may, in some embodiments, be windowed or filtered before or after correlation or convolution. Further, in some embodiments, the projections may be adjusted with a constant, linearly, quadratic, or higher order phase correction prior to reconstruction of the image.
To obtain an image of an object using the frequency swept method, additional steps may be performed to remove the ωRF(t) oscillations described above, since simple Fourier transformation of the time-domain signals may yield a spectrum (in this case, a projection of the object) that is contaminated by the frequency components of ωRF(t). In one embodiment, processing maybe done using a correlation method. Accordingly, the spin system response is treated as a linear system. As may be appreciated by one skilled in the art, adiabatic pulses are typically run in an adiabatic region. The adiabatic region is a non-linear region. In order to correlate the acquired signal as a linear system, it may be useful to perform excitation in a linear region such as a sub-adiabatic region. In some embodiments, excitation may be performed in a linear region.
The response r(t) of the linear system to the input function x(t) is the convolution process 50, shown in FIG. 4b, given by

r(t)=h(t){circle around (×)}x(t).  (8)

The linear system to which an input x(t) may be applied and from which a response r(t) comes. According to the standard nomenclature used in NMR, the unit impulse response h(t) is represented as the free induction decay (FID) and the unit frequency response function is the spectrum H(ω). These functions are related to one another by direct Fourier transformation. According to Fourier theory, the convolution in the time domain is a complex multiplication in the frequency co-domain:

F{r(t)}=R(ω)=H(ω)X(ω),  (9)

where X(ω) is a Fourier transformation of the input function x(t), which is the complex pulse function x(t) given by:

x(t)=ω1(t)exp(−i(ωRF(t)−ωc)t)  (10)

Alternatively, the spectrum of the system can be retrieved by using a correlation method 40, shown in FIG. 4a, which may be performed in the frequency domain with complex conjugate multiplication by the pulse function, as:




  
    
      
        
          H
          ⁡
          
            (
            ω
            )
          
        
        =
        
          
            
              
                R
                ⁡
                
                  (
                  ω
                  )
                
              
              ⁢
              
                
                  X
                  *
                
                ⁡
                
                  (
                  ω
                  )
                
              
            
            
              
                
                
                  X
                  ⁡
                  
                    (
                    ω
                    )
                  
                
                
              
              2
            
          
          .
        
      
    
    
      
        (
        11
        )
      
    
  




where |X(ω)| is the modulus of X(ω). The spectral profile of the HSn pulses is generally uniform within the bandwidth, and as a result, |X(ω)| is generally constant across the spectrum.

FIG. 5 illustrates one embodiment of a correlation method. FIG. 5 shows real parts of the response (Rx) 60 and the RF pulse spectrum (Xx) 62, and the real (Hx) 64 and imaginary (Hy) 66 parts of the system spectrum. These are shown in the frequency domain wherein the excitation amplitudes are weighted according to a step function, MO(ω) 68. Xx represents the Fourier transform of an RF pulse patter. Rx(ω) 60 has scrambled phase and contains contaminant signals arising from the ωRF(t) oscillations, which contain all frequencies in the spectral window. From a qualitative comparison, good correlation between Xx 62 and Rx 60 is apparent. The excitation profile of the HSn pulses is uniform within the bandwidth as result of |X(ω)| being generally constant across the spectrum. The spectrum of the system shown by Hx(ω) 64 generally replicates the spin density profile MO(ω) 68. The correlated absorption spectrum of the system Hx 64 was obtained from Equation 11 and by applying a first order phase correction on angle α(ω), where




  
    
      
        
          α
          ⁡
          
            (
            ω
            )
          
        
        =
        
          π
          ⁢
          
            
              (
              
                ω
                -
                
                  ω
                  c
                
              
              )
            
            
              ω
              c
            
          
          ⁢
          
            
              
                τ
                p
              
              dw
            
            .
          
        
      
    
    
      
        (
        12
        )
      
    
  




As shown in FIG. 5, contamination from wiggles are observed only in the imaginary part of the signal. Consequently, the real part is the spectrum which is the same as that obtained after Fourier transformation of an ordinary free induction decay and thus can be used for the spectroscopy or image reconstruction. Thus, in some embodiments, only the real part of the phased projections is used. In some embodiments, the complex projections can be used, for example with deleting the pulse contamination during reconstruction.

Generally, a projection has a central portion which generally comprises the quality segment and edges which have noise. Using correlation post processing, multiplication exacerbates the edge noise. Thus, post processing may further comprise eliminating the edge noise from the correlated signals such that the edge noise is eliminated from the subsequent image. Such elimination may comprise chopping, windowing, or zeroing of the portions of the projection having magnified noise.
During post processing, the projections may be biased to compensate for imperfections arising in data acquisition, such as timing errors, filter induced phase shifts, sample motion, flow, gradient instability, etc. To enhance consistency between different projections, a phase consistency or phase neutralization algorithm may be applied. This involves measuring the background noise in the different projections. The respective phases of the projections are then recomputed to neutralize any between projections phase variations. The noise can consistently be estimated by samples in that object that is either outside the object or completely in the background variation. New projections may be computed as:

μρ,θ={circumflex over (μ)}ρ,θexp(−i|ρ|>0.9 max(ρ){circumflex over (μ)}ρ,θ)   (13)

where {circumflex over (μ)}ρ,θ a represents each projection, with θ being the angular direction and ρ being the radius. A higher order correction may be used to minimize the imaginary part of the projections with a linear phase variation φθ:





  
    
      
        
          min
          
            φ
            μ
          
        
        ⁢
        
          
            
            
              imag
              ⁡
              
                (
                
                  
                    exp
                    ⁡
                    
                      (
                      
                        iφ
                        θ
                      
                      )
                    
                  
                  ⁢
                  
                    μ
                    
                      ρ
                      ,
                      θ
                    
                  
                
                )
              
            
            
          
          ⁢
          
            ∀
            ρ
          
        
      
    
    
      
        (
        14
        )
      
    
  




The minimization may be performed independently for each projection. This can be done to minimize artifacts that are predominantly carried by the imaginary part of the phased projections.

In alternative embodiments, complex phased projections may be used. While using only the real portion can improve the signal to noise ratio (by excluding pulsed feed through and artifacts due to the pulse), there may be situations where it is desirable to use the complex phased projections. For example, using complex phased projections may be advantageous in some forms of post processing and imaging—such as using the cone beam correction, discussed below, or gridding. Further, in embodiments wherein the complex phased projection is used, the imaginary part of the complex projection may be adjusted with a linear term, windowed, or zeroed.
FIGS. 4a and 4b illustrate post processing using correlation 40 and deconvolution 50 methods. In FIG. 4a, the excitation signal (x(t)) and the acquired time domain signal, (h(t)) are Fourier transformed followed by conjugate multiplication to generate a signal (H(w)). In FIG. 4b, the excitation signal (x(t)) and the acquired time domain signal (h(t)) are decorrelated and the decorrelated signal h(t)) is Fourier transformed to generate a resulting spectrum (H(w)). The processes illustrated in FIGS. 4A and 4B return the same signal (H(w)).
As previously described, first and second sequences may be run wherein gradient-, spin-, or simulated echoes are created in at least one of the sequences. The first and second sequences result in first and second acquisitions. Generally, the first acquisition comprises data from the pulse or sequence of pulses and the gradient and the second acquisition comprises data from the gradient. The data from the second acquisition can be subtracted from the data of the first acquisition. Thus, for example, if the first acquisition captures data relating to fast relaxing spins and slow relaxing spins and the second acquisition captures data relating to slow relaxing spins, subtracting the second acquisition data from the first acquisition data eliminates the slow relaxing spins and leaves only the fast relaxing spin contributions.
Post processing may further comprise suppressing artifacts and enhancing signal-to-noise ratio (SNR). Signal-to-noise ratio describes the relative contributions to a detected signal of the true signal and random superimposed signals or background noise. Suppressing artifacts and enhancing SNR may be done by performing a weighted averaging of neighboring projections, wherein neighboring projections have similar azimuthal angles. The frequency swept method generates a single combined image from a plurality of projections with each projecting being separated by a small azimuthal separation. Image reconstruction from a series of projections generally is undertaken under the influence of noise and systemic unknown errors. If unaltered, these unknown errors may cause significant image degradation. Systemic errors (SE) between the expected projections and the actual projections produce an error that cannot typically be averaged out using more acquisitions with the same parameters. Because the error is unknown, an error correcting algorithm is provided for minimizes the systemic errors (SE) and noise (SN). Specifically, a cone beam filtering and resampling algorithm is provided that corrects for both SE and SN.
In the cone beam filtering and resampling algorithm, each projection is replaced with a projection that is a combination of projections with small different (but not precisely known) views. The degree of error is controlled with




  
    β
    =
    
      
        γ
        ⁢
        
          
        
        ⁢
        
          1
          N
        
      
      ⁢
      
        |
        j
      
      ⁢
      
        θ
        j
      
    
  
  ,




where γ is a regularization scalar ( ̃1) and θj is the angle between a resampled projection and the assumed location of the measured projections. The index j is used over M nearest projections (and thereby the M smallest θj). The resampled projections are recalculated by:

The resampled projections are recalculated by





  
    μ
    j
  
  =
  
    
      ∑
      j
    
    ⁢
    
      
        w
        
          
            θ
            j
          
          +
          β
        
      
      ⁢
      
        
          μ
          ^
        
        j
      
    
  




with





  
    
      
        ∑
        j
      
      ⁢
      
        1
        
          
            θ
            j
          
          +
          β
        
      
    
    =
    
      1
      /
      w
    
  
  ,




wherein w is the normalizing unit weight. and {circumflex over (μ)}j denotes a set of measured projections with assumed directions. The cone beam filtering and resampling algorithm corrects for variations between the expected angles of projections and the actual projections by estimating new projections from different measured projections.

The processing discussed above is based on treatment of the acquired signal as a time domain signal. However, the excitation sweep is a function of both time and frequency and thus may be treated in either of the time domain or the frequency domain. In some embodiments, two spectra may be generated: one created by processing the signal as a time domain signal and one by processing the signal as a frequency domain signal. The two spectra have the same energy of noises, but different phases of noises. Thus, sensitivity of the magnetic resonance technique may be enhanced by averaging the two spectra.
Image Contrast
In the frequency swept excitation method, the magnetic field variation created by the applied gradient G can exceed other potential contributions (e.g., magnetic susceptibility differences and an inhomogeneous B0) such that their effects are not perceivable in images. Images developed using the frequency swept excitation method are generally unaffected by transverse relaxation, provided T2>10 dw (see FIG. 4). Under these conditions, the signal intensity depends only on T1 and spin density (M0) as:




  
    
      
        S
        =
        
          
            M
            0
          
          ⁢
          
            
              1
              -
              
                E
                1
                SWIFT
              
            
            
              1
              -
              
                
                  E
                  1
                  SWIFT
                
                ⁢
                cos
                ⁢
                
                  
                
                ⁢
                
                  (
                  θ
                  )
                
              
            
          
          ⁢
          
            
              sin
              ⁡
              
                (
                θ
                )
              
            
            .
          
        
      
    
    
      
        (
        15
        )
      
    
  




For fixed TR, the maximum signal intensity is attained with optimum flip angle θopt which satisfies the equation

cos(θopt)=E1SWIFT.  (16)

T1 contrast can be evaluated from the derivative of the signal,





  
    
      d
      S
    
    
      d
      
        (
        
          1
          /
          
            T
            1
          
        
        )
      
    
  
  .




For fixed TR, this derivative has a maximum at θ≈1.7θopt. A good compromise between sensitivity and contrast thus occurs in the range θopt<θ<1.7θopt, where θopt corresponds to a spin of interest which has the smallest T1 value. For the case of θ<θopt, T1-weighting becomes negligible, and image contrast is dictated mainly by spin density variations.

As previously discussed, a plurality of frequency sweeps may be run using a frequency swept pulse and reversing the direction of the frequency sweep and/or changing the sign of the gradient to minimize chemical shift artifacts. Post processing may further be done to improve image quality and achieve fat/water separations.
In fat/water separation the dependence on spatial shift of off-resonance isochromats is exploited for separation. The direction of the spatial shift is identical to the orientation of the magnetic field gradient during readout. By changing the orientation of the magnetic field gradient during readout the fluctuation of the off-resonance isochromat can be separated from the consistent location of the on-resonance isochromat. The algorithm can be prescribed by a set of algebraic equations. Such a separation can be performed equally well on the sinogram as the FT of the projections. The often small spatial shift can be better utilized when the algebraic equations are combined with regularization to reduced undue noise amplification.
In embodiments wherein one of the excitation frequency or the acquisition frequency has been jittered, it may be desirable to unjitter. Jittering of the carrier frequency can be done to shift the resulting spectra in an inverse direction before image reconstruction. Unjittering may be done during post processing and may be achieved by a linear phase in the time domain or a shift in the projection domain
EXAMPLES
Computer simulations based on the classical Bloch equations can help to reveal the behavior of spins during the application of amplitude- and/or frequency-modulated pulses as taught herein. FIG. 3 illustrates the oscillatory motion 30 of the magnetization components of a given isochromat having frequency ω. of the isochromat excitation time in FIG. 3 is shown by the vertical dotted line 32. In FIG. 3,MXPM(t) 34 presents the x-axis component in the transverse magnetization vector of the isochromat in a reference frame as is known as the phase-modulated (PM) frame, which rotates around the static magnetic field direction (z) in an angular velocity ωc equal to the center frequency in the sweep range. MXFM(t) 36 is the x-axis component in a frequency-modulated (FM) frame, which rotates synchronously with the (time-dependent) pulse frequency ωRF(t). FIG. 3 also shows the absolute value of the transverse magnetization




  
    
      M
      xy
    
    ⁡
    
      (
      t
      )
    
  
  ⁢
  
    (
    
      
        
          
            M
            x
            2
          
          ⁡
          
            (
            t
            )
          
        
        +
        
          
            M
            y
            2
          
          ⁡
          
            (
            t
            )
          
        
      
    
    )
  
  ⁢
  38.




The PM frame rotates at a constant carrier frequency ωc, whereas the FM frame rotates in synchrony with the pulse frequency ωRF(t). In the FM frame the orientation of ω1(t) remains stationary during an frequency swept passage. The transformation between two frames is done by:





  
    
      
        
          
            
              M
              x
              
                F
                ⁢
                
                  
                
                ⁢
                M
              
            
            ⁡
            
              (
              t
              )
            
          
          +
          
            
              iM
              y
              
                F
                ⁢
                
                  
                
                ⁢
                M
              
            
            ⁡
            
              (
              t
              )
            
          
        
        =
        
          
            (
            
              
                
                  M
                  x
                  PM
                
                ⁡
                
                  (
                  t
                  )
                
              
              +
              
                iM
                y
                PM
              
            
            )
          
          ⁢
          
            exp
            ⁡
            
              (
              
                
                  -
                  i
                
                ⁢
                
                  
                
                ⁢
                
                  φ
                  ⁡
                  
                    (
                    t
                    )
                  
                
                ⁢
                t
              
              )
            
          
        
      
    
    
      
        
          (
          17
          )
        
        ⁢
        
          
        
      
    
  




where φ(t)=(ωRF(t)−ωc)t+π/2. The constant π/2 term arises because the rotated vector is perpendicular to the direction of the RF field. In FIG. 3, MxPM(t) 34 presents the x-axis component of the transverse magnetization vector of the isochromat in phase-modulated (PM) reference frame, which rotates around the static magnetic field direction (z) with an angular velocity ωc equal to the center frequency in the sweep range. MxFM(t) 36 is the x-axis component in a frequency-modulated (FM) frame, which rotates synchronously with the (time-dependent) pulse frequency ωRF(t).

As discussed previously, the frequency swept excitation method sequence has less stringent constraints than indicated by Eqs. (6a) and (6b). First, because the pulse is segmented, the average value of ω1(t) scales inversely with τp/dw. Second, according to simulation and experimental data, the correlation method works well up to a rotation angle near 90° before significantly violating the linearity condition of Eq. (6b). The frequency swept excitation method is not restricted to the rapid passage region by Eq. (6a). For example, the frequency swept excitation method may also be used in the intermediate passage, linear region, with the consequences of sacrificing signal-to-noise ratio (S/N) and resolution. To illustrate this point, FIG. 6 presents the excitation performance of the HS1 pulse in the intermediate passage region. The simulated parameter A0cor is the normalized amplitude of the FID obtained by inverse FT of the correlated spectra. A0cor is normalized to be equal to 1 for T2∞, A0cor is plotted against T2/(τp+τa) using different excitation flip angle θ (θ calculated for T2∞). The function E2=exp(−(τp+τa)/T2) (solid line) well describes the dependencies. From this simulation, it can be seen that the limit of the T2 sensitivity of the SWIFT sequence is T2>τp+τa  ̃dw.
While the frequency swept excitation method may be used in a variety of applications, the method is demonstrated for imaging spins with extremely short T2 values (FIGS. 7 and 8). The first test object, shown in FIG. 7, is thermoplastic 90, which is invisible by conventional MRI because the T2 value is extremely short ( ̃0.3 ms). As can be seen from FIG. 7, the frequency swept excitation method produced a highly resolved 3D image of the object. The images 92, 94 were obtained using a standard MRI scanner (4.7 T) which is not equipped with special software or hardware (e.g., solid state accessory).
Frequency swept excitation images of ex vivo bovine tibia 80 were also acquired to demonstrate the technique's sensitivity to short T2 spins (FIG. 8). This image is compared to an image acquired using the shortest TE. value (1.6 ms) that could be attained with a standard gradient-echo sequence. The cortical compact bone, which has T2=0.4 ms, is not visible in the gradient-echo image 82 (FIG. 8), but is easily recognizable in the frequency swept excitation image 84 (FIG. 8).
These frequency swept excitation images were reconstructed using a standard 3D back-projection algorithm for 92, 94 of FIG. 7 and gridding for 84 of FIG. 8, with no additional processing (e.g., filtering) to remove subtle image intensity ripples and other minor artifacts.
FIG. 9 illustrates images 100 of molar tooth decay made using the frequency swept excitation method. To create the images of FIG. 9, the following parameters were used: sw=62 kHz, 256×128×32, D=3 cm, 32 averages, total time=10 min, 4.7T. As may be appreciated, teeth are particularly hard to image using MRI techniques because most parts of the tooth (excluding, for example, the root) have very fast relaxing spins. While CW techniques can be used to image teeth, they typically take on the order of 10 hours. In contrast, using the frequency swept method, teeth were imaged in a total time of 10 minutes.
Although the invention has been described with reference to specific embodiments, persons skilled in the art will recognize that changes may be made in form and detail without departing from the spirit and scope of the invention.

## Claims

1. A method comprising: applying a sweeping frequency excitation having a duration, the sweeping frequency excitation being configured to sequentially excite isochromats having different resonant frequencies; applying a first gradient while applying the sweeping frequency excitation; acquiring a time domain signal during the duration, the time domain signal being based on evolution of the isochromats; and; achieving a steady, oscillating, or pseudo-steady state; calculating a projection angle or plane using a gradient shape and frequency sweep; and using the acquired time domain signal to create a magnetic resonance image.

2. The method of claim 1, wherein the first gradient is constant.

3. The method of claim 1, wherein the first gradient is shaped.

4. The method of claim 1, further comprising calculating a projection angle trajectory or plane using a gradient shape and frequency sweep.

5. The method of claim 1, further comprising changing an orientation of the first gradient.

6. The method of claim 5, further comprising separating a fluctuation of an off-resonance isochromat with a consistent location of an on-resonance isochromat.

7. The method of claim 1, further comprising jittering at least one of the sweeping frequency excitation and the time domain signal.

8. The method of claim 7, further comprising unjittering the at least one of the sweeping frequency excitation and the time domain signal that was jittered.

9. The method of claim 1, wherein applying a sweeping frequency excitation is done to coincide with a motion of interest.

10. The method of claim 1, wherein achieving a steady, oscillating, or pseudo-steady state is done before applying a sweeping frequency excitation.

11. The method of claim 10, wherein achieving a steady, oscillating, or pseudo-steady state comprises applying a preparation pulse.

12. The method of claim 11, further comprising acquiring a plurality of preparation time domain signals.

13. The method of claim 11, further comprising applying a preparation gradient.

14. The method of claim 13, further comprising acquiring a preparation plurality of time domain signals wherein acquiring the plurality of preparation time domain signals is done with sequential gradient orientations.

15. The method of claim 13, further comprising acquiring a plurality of preparation time domain signals wherein acquiring the plurality of preparation time domain signals is done with random or pseudo-random gradient orientations.

16. The method of claim 13, wherein the preparation gradient is reversed during the preparation pulse.

17. The method of claim 11, wherein the preparation pulse is a radio frequency pulse.

18. The method of claim 11, further comprising varying radio frequency power during the preparation pulse.

19. The method of claim 1, further comprising using a digital filter while acquiring a time domain signal to limit the acquired signal.

20. The method of claim 1, wherein the sweeping frequency excitation is asymmetrical.

21. The method of claim 1, further comprising processing the acquired time domain signal.

22. The method of claim 1, further comprising applying a magnetic field during applying the sweeping radio frequency excitation.

23. The method of claim 1, further comprising generating a first spectra based on a correlation of a Fourier transform of the applied sweeping frequency excitation and a Fourier transform of the acquired time domain signal.

24. The method of claim 23, further comprising generating a second spectra based on processing the acquired time domain signal as a frequency domain signal and further comprising averaging the first and second spectra.

25. The method of claim 1, further comprising generating a first spectra based on deconvoluting the applied sweeping frequency excitation and the acquired time domain signal to generate a deconvoluted signal and Fourier transforming the deconvoluted signal.

26. The method of claim 25, further comprising generating a second spectra based on processing the acquired time domain signal as a frequency domain signal and further comprising averaging the first and second spectra.

27. The method of claim 1, wherein applying the sweeping frequency excitation comprises applying a phase modulation.

28. The method of claim 1, wherein applying the sweeping frequency excitation comprises applying a frequency modulation.

29. A method comprising: applying a sweeping frequency excitation having a duration, the sweeping frequency excitation being configured to sequentially excite isochromats having different resonant frequencies; applying a first gradient while applying the sweeping frequency excitation; acquiring a time domain signal during the duration, the time domain signal being based on evolution of the isochromats wherein acquiring a time domain signal comprises capturing or freezing motion along a direction of the first gradient; achieving a steady, oscillating, or pseudo-steady state; and using the acquired time domain signal to create a magnetic resonance image.

30. A method comprising: applying a sweeping frequency excitation having a duration, the sweeping frequency excitation being configured to sequentially excite isochromats having different resonant frequencies; applying a first gradient while applying the sweeping frequency excitation; acquiring a time domain signal during the duration, the time domain signal being based on evolution of the isochromats; and; achieving a steady, oscillating, or pseudo-steady state; applying a second gradient and acquiring a second time domain signal, the second time domain signal being based on evolution of the isochromats, wherein the second gradient is opposite the first gradient; and using the acquired first and second time domain signals to create a magnetic resonance image.

31. The method of claim 30, further comprising creating a gradient-echo, a spin-echo, or a simulated-echo.

32. The method of claim 31, further applying a second sweeping frequency excitation having a duration wherein the first sweeping frequency excitation results in a first sequence and the second sweeping frequency excitation results in a second sequence, and further comprising subtracting the second sequence from the first sequence.

33. The method of claim 30, further comprising filtering spin-spin relaxation times based on the created gradient-echo, spin-echo, or simulated-echo.

34. A method comprising: applying a sweeping frequency excitation having a duration, the sweeping frequency excitation being configured to sequentially excite isochromats having different resonant frequencies; applying a first gradient while applying the sweeping frequency excitation; acquiring a time domain signal during the duration, the time domain signal being based on evolution of the isochromats; and; achieving a steady, oscillating, or pseudo-steady state; and processing the acquired time domain signal; wherein achieving a steady, oscillating, or pseudo-steady state includes correcting for a lack of a steady state and is done during processing the acquired time domain signal; and using the acquired time domain signal to create a magnetic resonance image.

35. A method comprising: applying a sweeping frequency excitation having a duration by applying a plurality of discrete excitation pulses, the sweeping frequency excitation being configured to sequentially excite isochromats having different resonant frequencies; applying a first gradient while applying the sweeping frequency excitation; acquiring a time domain signal during the duration, the time domain signal being based on evolution of the isochromats; and; achieving a steady, oscillating, or pseudo-steady state; and wherein acquiring the time domain signal includes sampling between excitation pulses; and using the acquired time domain signal to create a magnetic resonance image.