This application relates generally to magnetic resonance imaging, and more particularly to radio frequency mapping for magnetic resonance imaging.
Inhomogeneity of the radio frequency (RF) field causes variation of flip angle with spatial location. This flip angle variation may result in variable image intensity or failure of flip-angle-sensitive techniques such as fat saturation.
Measurement of flip angle can be used to correct image intensity variation caused by B1 field inhomogeneity. Measurement of flip angle is also useful to obtain correct results in T1 mapping with multiple-flip-angle techniques. Measurement of both flip angle and relative phase of the B1 field is also necessary for the design of RF waveforms for multiple simultaneous transmitter systems.
Mapping of the B1 field has been performed using double angle methods. In these methods, two spin-echo or gradient recalled echo (GRE) acquisitions are performed. In a spin-echo double angle method, a first acquisition M1 is performed with a α-2α sequence, and a second acquisition M2 is performed with a 2α-4α sequence. Dividing the magnitude of the first acquisition by the magnitude of the second acquisition gives a function of flip angle α as follows:
from which the flip angle α can be calculated as
α=sec−1{square root over (8M1/M2)} (2)
In GRE double angle methods, two GRE acquisitions are performed with flip angles α and 2α. Dividing the magnitudes of the two acquisitions gives a function of flip angle α as follows:
Equations (1) and (3) assume that the repetition time (TR)→∞.
Other B1 mapping methods which derive estimates of B1 from signal intensities have been developed. One method utilizes two acquisitions with the same flip angle but alternating variable short sequence repetition time (TR). Another method uses three GRE acquisitions with flip angle distributed around 180° and fits the observed signal intensity to the expected 180° signal null. In another technique, flip angle is calculated from the ratio of a spin echo and a stimulated echo, similar to double angle methods but with both echoes obtained during the same sequence repetition.
The disclosure provides phase-sensitive methods of radio frequency field mapping (e.g., B1 mapping), in which flip angle is encoded in the phase of a transverse magnetization produced by a series of RF pulses. The phase-sensitive methods can measure flip angle over a wider range than other methods such as double-angle methods.
In one aspect, a phase-sensitive method of radio frequency mapping comprises acquiring a first transverse magnetization phase measurement using an RF excitation pulse with flip angle 2α followed immediately by an RF excitation pulse with flip angle α about an orthogonal axis and acquiring a second transverse magnetization phase measurement using an RF excitation pulse with flip angle −2 α followed immediately by an RF excitation pulse with flip angle α about an orthogonal axis. The method further comprises computing a phase difference between the two phase measurements and generating a radio frequency map based on the phase difference. The radio frequency map may be used, for example, to correct an image for variation in image intensity caused by B1 field inhomogeneity. The radio frequency map may also be used to correct T1 measurements for variations caused by B1 field inhomogeneity. The corrected T1 measurements may be used for T1-weighted imaging, which provides contrast between tissues with different T1 relaxation times.
Additional features and advantages of the invention will be set forth in the description below, and in part will be apparent from the description, or may be learned by practice of the invention. The advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
It is to be understood that both the foregoing summary of the invention and the following detailed description are exemplary and explanatory and are intended to provide further explanation of the invention as claimed.
The accompanying drawings, which are included to provide further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate aspects of the invention and together with the description serve to explain the principles of the invention.
In this disclosure, a B1 field may be a radio frequency magnetic field that is generated by an RF coil and is approximately orthogonal to a main field (B0) of an MRI machine. The B1 field may also oriented at other angles with respect to the main field B0 besides being orthogonal to the main field B0.
In the absence of main field (B0) inhomogeneity, the initial 2α pulse about the x axis rotates the initial longitudinal magnetization M0 into the y-z plane. The subsequent α flip about the y axis brings the magnetization toward the transverse (x-y) plane, where the flip angle of the initial 2α pulse is reflected in the phase angle of the resulting transverse magnetization Mxy.
For the case of zero B0 inhomogeneity, the excitation can be modeled as a constant rectangular excitation pulse with duration 2τ giving a (left-handed) flip angle of 2αx followed by a constant rectangular pulse of duration τ giving a (left-handed) flip angle of αy. Given an initial longitudinal magnetization of M0{circumflex over (z)} and neglecting relaxation effects, this sequence of excitations gives the following resulting magnetization:
Mx=−M0 sin α cos 2α
My=M0 sin 2α
Mz=M0 cos α cos 2α (4)
The transverse component Mxy=Mx+iMy is plotted at different flip angles in
For nonuniform B0 field, the form of Equation (4) changes. In this case, the first 2αx excitation pulse can be modeled as a left-handed flip of angle 2√{square root over (α2+Δω2τ2)} about the vector [2α, 0, 2Δωτ], where Δω is off-resonance frequency for a given location in the imaging volume caused by B0 field inhomogeneity or chemical shift. The second αy excitation pulse can be modeled as a left-handed flip of angle √{square root over (α2+Δω2τ2)} about the vector [0, α, Δωτ]. Given initial magnetization M0{circumflex over (z)} and neglecting relaxation, the resulting magnetization is:
with β=√{square root over (α2+Δω2τ2)} and ± representing + when the pulse in the x axis is 2α. A modification to the pulse sequence in which ± represents − in Equation (5) is described below. The transverse component Mxy=Mx+iMy is plotted for various values of flip angle α and off-resonance precession angle Δωτ in
Although Mxy varies with off-resonance due to B0 field inhomogeneity, the phase of Mxy remains a good function of flip angle α over a wide range of off-resonant frequencies. However, off-resonance frequency Δω must be known for each point in the imaging volume to correctly estimate α from the phase of Mxy. This requirement can be met by using a rapid gradient-recalled echo sequence to produce a B0 field map.
In practice, the phase of Mxy cannot be measured with a single acquisition because the image phase depends on several factors in addition to the flip angle α. For instance, the image phase will reflect retarded potentials of the propagating RF wave within the body as well as the effects of eddy currents. Phase effects from retarded potentials become larger at higher field strengths. These sources of phase can be removed from the measurement of the phase of Mxy by a second acquisition in which the 2αx pulse is reversed in sign. In this aspect, the second acquisition is performed with a second pulse sequence comprising a −2αx excitation pulse about the x axis followed by an αy excitation pulse. The ± in
The phase of the second acquisition is subtracted from the phase of the first acquisition. This subtraction removes sources of phase other than flip angle α. The transverse magnetization Mxy for the first acquisition is denoted as Mxy+ and the transverse magnetization Mxy for the second acquisition is denoted as Mxy−. The difference in phase between the two acquisitions is denoted:
θ=∠Mxy+−∠Mxy− (6)
where phase of Mxy is given by tan−1(My/Mx).
For the case of no B0 field inhomogeneity described by Equation (4), changing the sign of the 2αx pulse changes only the sign of My, leaving Mx and Mz unchanged. Thus ∠Mxy−=−∠Mxy+ and the phase difference θ is given by:
θ=∠Mxy+−∠Mxy−=2∠Mxy+ (7)
When B0 field inhomogeneity is present, the expression for θ becomes more complicated. The transverse magnetization for the second acquisition, with the initial 2α excitation reversed in sign, is given by Equation (5) where ± terms represent −. The resulting transverse magnetization Mxy is shown in
The phase difference θ is plotted for a range of flip angles α and a range of off-resonance accrual angles Δωτ in
In one aspect, the phase-sensitive B1 mapping method described above was implemented with both GRE and echo-planar readout schemes. Phase unwrapping of θ was performed for studies showing greater than 90° variation in α using a method based on the solution of the Poisson equation. Because the closed form expression of θ is quite complicated, a lookup table of calculated values of θ versus α for the appropriate value of Δωτ was used to form the estimate of α at each image location.
Equation (5) shows that the sign and magnitude of Mz at the end of the excitation will vary with flip angle α, and some values of α will result in negative values of Mz. A series of (nominally) 90° tips followed by large dephasing gradient lobes were used at the end of the acquisition window to allow saturation recovery of Mz from zero rather than a negative value.
Experimental verification of Equation (5) was performed by running the B1 mapping sequence with GRE acquisition and long TR on a small vial of copper sulfate doped agar within a receive-only head coil of a 3.0T Siemens Trio imaging system. Excitation was performed with the body coil. Because of the small size of the phantom, nearly uniform flip angle was achieved over the phantom volume. The sequence was run with positive 2α flip about x axis, and the resulting transverse magnetization Mxy averaged over a volume of the phantom was measured for various values of α, the results of which are shown in
A phantom study was performed to map the RF field of a commercially available transmit-receive extremity imaging coil on the 3T Siemens Trio imaging system. For this experiment, a phantom was constructed which nearly filled the bore of the coil. The phantom was filled with agar which was doped with copper sulfate to give an approximate T1 of 260 ms and approximate T2 of 50 ms. The phantom was also doped with a physiologic concentration of NaCl to simulate coil loading by soft tissue. The phase-sensitive B1 mapping method was used to image in the axial plane (shown in
An in vivo B1 mapping experiment was performed with the phase-sensitive method, showing the flip angle achieved by a commercially available transmit-receive head coil in a healthy volunteer. This study was performed with written informed consent under the direction of the local Institutional Review Board (IRB). For this experiment, a 3D GRE acquisition was performed (64×51×32 matrix size, 22×17.9×32 cm FOV, TR=121 ms, TE=5.3 ms, imaging time 3:20 for each of two acquisitions for total imaging time of 6:40).
The phantom studies shown in
The phase-sensitive method is able to measure a much wider range of flip angles than the double angle method.
Because the ratio M1/M2 used in the double angle method to calculate flip angle α varies slowly near α=0°, the double angle method is sensitive to noise at low flip angles. This poor performance at low flip angles is well demonstrated in
The phase-sensitive B1 mapping method according to aspects of the disclosure and existing double angle methods are equivalent with respect to imaging time for 3D imaging. Both have magnetization preparation steps with similar TR requirements. Both can be followed by a variety of readout schemes. Imaging time depends primarily on the readout scheme used. For ease of implementation, the phase-sensitive method has been demonstrated with gradient recalled echo readout and with echo-planer readout with short echo train length. These readout schemes are not optimal for imaging time but have allowed straightforward implementation and demonstration of the performance of the phase-sensitive B1 mapping method. Imaging time may be reduced by implementation of faster acquisition schemes such as echo-planar readout with longer echo train lengths or spiral echo-planar readout.
B1 measurement with either the phase-sensitive method or with existing double angle methods requires relatively long TR. With double angle methods, B1 maps are formed by measuring the magnitude of the signal after α or 2α excitation. This signal amplitude depends on T1, TR, and the flip angles of preceding excitations. The effects of the preceding T1 and preceding excitation history can be removed by using very long TR, typically greater than 5 times the maximum T1 expected in the sample. Alternatively, presaturation has been performed with a recovery period before to the double angle excitation, to allow “resetting” of the longitudinal magnetization to zero before each excitation. This allows shortening of the TR without affecting the validity of the B1 estimate. Shortening TR allows less time for signal regeneration after presaturation, lowering the signal-to-noise ratio. Thus, relatively long TR is still necessary to allow signal regeneration for adequate B1 estimation with double angle methods.
The phase-sensitive method of B1 mapping is largely independent of T1, TR, and prior excitation history because only the phase of the transverse magnetization is used to form the B1 estimate. The signal magnitude does not enter into the calculation of flip angle with this method. However, for some flip angles the longitudinal magnetization Mz available at the beginning of a sequence repetition has been inverted by the prior excitation, giving inverted phase of transverse magnetization on the subsequent excitation. Thus, if the phase-sensitive method is used with short TR, the measured phase from which the B1 map is calculated will oscillate with each acquisition by +/−π for some flip angles. This oscillation may be more a tractable problem than the complicated dependence of signal magnitude on T1, TR, and prior excitation history which is faced by double angle methods at low TR. It is possible that this oscillation can be taken into account to allow the phase sensitive method to be used with short TR. However, straightforward implementation of the phase-sensitive method, like the double angle methods, requires either long TR relative to the maximum expected T1 or presaturation to remove the effect of the prior excitation on the sign of Mz. For the results discussed in this disclosure, presaturation was performed as described above.
Because both the double angle and phase-sensitive B1 mapping methods require moderately long TR, imaging speed with either of these methods relies primarily on the acquisition scheme used. Presaturated double angle B1 mapping with reduced imaging time has been achieved by using slice selective excitation and rapid spiral data acquisition. This rapid readout scheme could be applied to the phase-sensitive method to give a similar reduction of imaging time.
In aspects of the disclosure, the phase-sensitive method is applicable to 3D imaging, as the RF pulses are nonselective. Nonselective excitation is used to minimize the duration of excitation, to allow B1 mapping over a wide range of B0 inhomogeneity. Nonselective excitation necessitates large imaging volumes, which leads to low resolution or long scan time. Slab selective excitation with high bandwidth pulses for spatially localized 3D imaging could be implemented in the phase-sensitive method for greater ease and flexibility of scan volume prescription. This would cause some increase in RF pulse length, with some resulting narrowing of the range of B0 inhomogeneity over which the method is valid.
Those skilled in the art will appreciate that the systems and methods described in connection with the embodiments disclosed herein may be implemented or performed with general purpose processors, a digital signal processors (DSPs), application specific integrated circuit (ASICs), field programmable gate array (FPGAs), logic programmable devices, discrete hardware components, or any combination thereof. Further, the algorithms performed by the RF coils, gradient coils, and associated amplifiers and controllers may be embodied in software executed by a processor, directly in hardware, or a combination thereof. The software may be stored in memory or any computer-readable storage medium known in the art.
Those of skill in the art would appreciate that the various illustrative blocks, modules, elements, components, methods, and algorithms described herein may be implemented as electronic hardware, computer software, or combinations of both. Furthermore, these may be partitioned differently than what is described. To illustrate this interchangeability of hardware and software, various illustrative blocks, modules, elements, components, methods, and algorithms have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the overall system. Skilled artisans may implement the described functionality in varying ways for each particular application.
It is understood that the specific order or hierarchy of steps or blocks in the processes disclosed is an illustration of exemplary approaches. Based upon design preferences, it is understood that the specific order or hierarchy of steps or blocks in the processes may be rearranged. The accompanying method claims present elements of the various steps in a sample order, and are not meant to be limited to the specific order or hierarchy presented.
The previous description is provided to enable any person skilled in the art to practice the various aspects described herein. Various modifications to these aspects will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other aspects. Thus, the claims are not intended to be limited to the aspects shown herein, but is to be accorded the full scope consistent with the language claims, wherein reference to an element in the singular is not intended to mean “one and only one” unless specifically so stated, but rather “one or more.” All structural and functional equivalents to the elements of the various aspects described throughout this invention that are known or later come to be known to those of ordinary skill in the art are expressly incorporated herein by reference and are intended to be encompassed by the claims. Moreover, nothing disclosed herein is intended to be dedicated to the public regardless of whether such invention is explicitly recited in the claims. No claim element is to be construed under the provisions of 35 U.S.C. §112, sixth paragraph, unless the element is expressly recited using the phrase “means for” or, in the case of a method claim, the element is recited using the phrase “step for.”
This invention was made with government support under Grant #K08 CA112449 awarded by the National Institutes of Health. The Government has certain rights to this invention.
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