# Patent

## Title
B1 mapping in MRI system using k-space spatial frequency domain filtering

## Abstract

Frequency filtering of spatially modulated or “tagged” MRI data in the spatial frequency k-space domain with subsequent 2DFT to the spatial domain and pixel-by-pixel arithmetic calculations provide robust ratio values that can be subjected to inverse trigonometric functions to derive B1 maps for an MRI system.

## Background
BACKGROUND
1. Technical Field
This application describes methods and apparatus for generating multi-dimensional maps of the spatial distribution of radio frequency (RF) magnetic fields (typically labeled as the “B1” field) in MRI (magnetic resonance imaging) systems.
2. Related Art
Magnetic resonance imaging (MRI) systems are by now well known and many different types of commercially available MRI systems are regularly employed for medical research and/or diagnostic purposes. Although there are many variations in detailed image acquisition processes and/or MRI system geometries, they all share some basic fundamental principles.
For example, MRI systems all utilize the principle of nuclear magnetic resonance (NMR) wherein nuclei having a net magnetic moment (e.g., nuclei having an odd number of protons such as the hydrogen nucleus) are immersed in a static background magnetic field B0. Ideally, this background static magnetic field is homogeneous throughout a volume to be imaged (even in the presence of the intervening object to be imaged). This background magnetic field tends to align a significant number of the nuclei magnetic moments therewith so as to produce a rather significant net nuclei magnetization aligned with the homogeneous background magnetic field B0.
The nuclear magnetic moments can be thought of as rotating about an axis at a frequency which is proportional to the magnetic field imposed upon the nucleus at its particular spatial location. The so-called Larmor angular frequency ω=γβ where γ is a gyromagnetic ratio constant for a given species of nuclei and its structural environment and β is the strength of the imposed magnetic field. Accordingly, in an ideal world, a particular species of nuclei having common physical surroundings would all have a common Larmor frequency of rotation. However, by superimposing an auxiliary magnetic field having a linear gradient (e.g., in one of three orthogonal directions x, y, z), it will be appreciated that the Larmor frequency of such common species of nuclei disposed along the changing field gradient will now have different values in accordance with the magnitude of the linear magnetic gradient field at the spatial location of a given nucleus. Again, in an ideal world, such superimposed magnetic gradient field would have only an exactly linear gradient in one desired dimension and otherwise be uniform and homogeneous. Typically, an MRI system has three sets of gradient coils arranged to impose linear magnetic gradient fields in each of three different mutually orthogonal directions.
By transmitting an RF magnetic field at the Larmor frequency into the volume that is to be imaged, one can selectively “excite” the nuclear magnetic resonant (NMR) nuclei that happen to fall within a given selected volume (e.g., a “slice”) so as to nutate the nuclear magnetic moment away from the nominal static magnetic field B0. Depending upon the amplitude and duration of such an exciting RF pulse, the magnetic moment of a nucleus can be “nutated” away from the nominal B0 alignment by controlled amounts (e.g., 90°). After such nutation, the nuclear magnetic moment tends to relax back toward nominal alignment with B0, but with characteristic longitudinal and transverse time constants T1, T2 and, in the process, each relaxing nuclear magnetic moment emits a radio frequency response signal that can be detected as an RF signal having a particular amplitude, frequency and phase (e.g., relative to the exciting RF field and/or to other NMR nuclei emitting RF response signals).
By carefully choosing a particular “MRI sequence” of RF excitation pulse(s) and magnetic gradient pulses, one can elicit meaningful spatially-encoded RF response signals so as to permit construction of an image or map of the NMR nuclei densities throughout a specific volume of the MRI system (e.g., a slice of the “imaging volume”). Over the last several decades of MRI system development, a very large number of MRI sequences have been discovered and commercialized. Since most, if not all, such imaging sequences can be utilized in the following exemplary embodiments, and since such are already well known to those skilled in the art, further detail about specific MRI sequences is not required.
The RF excitation fields transmitted into the imaging volume as well as the RF response fields received from the imaging volume are transmitted and/or received via RF coils which act as RF antennae. Once again, there are many different RF coil geometries well known to those in the art. For example, there may be “head” coils, “surface” coils, “whole body” coils, “multi-coil arrays” and the like. All of these RF antennae/coil structures serve to transduce electromagnetic radio frequency waves to/from NMR nuclei in the imaging volume onto feed line(s) of the RF antennae/coils which are then connected appropriately to RF transmitter and/or receiver circuits (e.g., via a transmit/receive switch if the same coil structure is used to both transmit and receive), as will be apparent to those skilled in the art.
Once again, in a perfect world, the RF antennae/coil sensitivity throughout the volume to be imaged is desirably absolutely uniform and homogeneous at all points within the volume to be imaged.
Unfortunately, the ideals of absolutely uniform homogeneity, absolutely linear gradients, etc., desired for various magnetic/RF fields in the MRI system are not realized in practice. Accordingly, various “shimming” attempts are made to correct for unwanted departures from the ideal and/or to compensate acquired signals that have been adversely affected by such less than ideal circumstances.
This application is directed towards a new and improved technique for mapping of the RF B1 magnetic field associated with transmit sensitivity of the RF antennae/coils of an MRI system. Various prior techniques have been used for generating such B1 maps which are then used either to improve the design of the MRI system itself and/or to provide compensated output images from the MRI system (e.g., especially where quantitative measurements are to be made based upon such images). However, as will be explain below, such prior techniques leave room for improvement—which the exemplary embodiments explained in detail below provide.
Some examples of prior approaches that may be relevant to the present application are identified below:

    
    
        1. L. Axel, L. Dougherty, “MR Imaging of Motion with Spatial Modulation of Magnetization,” Radiology, Vol. 171, pages 841-845 (1989)
        2. L. Axel, L. Dougherty, “Heart Wall Motion: Improved Method of Spatial Modulation of Magnetization for MR Imaging,” Radiology, Vol. 172, pages 349-350 (1989)
        3. E. K. Insko, L. Bolinger, “Mapping of the Radiofrequency Field,” J Magn Reson (A), Vol. 103, pages 82-85 (1993)
        4. R. Stollberger, P. Wachs, “Imaging of the Active B1 Field in Vivo,” Magn Reson Med, Vol. 35, pages 246-251 (1996)
        5. N. G. Dowell, P. S. Tofts, “Fast, Accurate, and Precise Mapping of the RF Field In Vivo Using the 180° Signal Null,” Magn Reson Med, Vol. 58, pages 622-630 (2007)
        6. F. Jiru, U. Klose, “Fast 3D Radiofrequency Field Mapping Using Echo-Planar Imaging,” Magn Reson Med, Vol. 56, pages 1375-1379 (2006)
        7. J. T. Vaughan, M. Garwood, C. M. Collins, W. Liu, L. DelBarre, G.
    
    


Adriany, P. Anderson, H. Merkle, R. Goebel, M. B. Smith, K. Ugurbil, “7T vs. 4T: RF Power, Homogeneity, and Signal-to-Noise Comparison in Head Images,” Magn Reson Med, Vol. 46, pages 24-30 (2001)

    
    
        8. J. Wang, W. Mao, M. Qiu, M. B. Smith, R. T. Constable, “Factors Influencing Flip Angle Mapping in MRI: RF Pulse Shape, Slice Select Gradients, Off-Resonance Excitation, and B0 Inhomogeneities,” Magn Reson Med, Vol. 56, pages 463-468 (2006)
        9. V. L. Yarnykh, “Actual Flip Angle Imaging in the Pulses Steady State: A Method for Rapid Three-Dimensional Mapping of the Radiofrequency Field,” Magn Reson Med, Vol. 57, pages 192-200 (2007)
        10. M. A. Bernstein, K. F. King, X. J. Zhou, Handbook of MRI Pulse Sequences, Elsevier Academic Press, especially pages 166-171 (2004)
        11. X. Chen, X. Shou, W. R. Dannels, “Feasibility of Rapid B1 Mapping with RF Prepulse Tagging,” Proceedings of ISMRM, 16th Scientific Meeting, Toronto, Canada, May 2008 Abstract #3045
        12. X. Chen, X. Shou, W. R. Dannels, “Feasibility of Rapid B1 Mapping with RF Prepulse Tagging,” poster presented at Research Showcase 2008, Case Western Reserve University, Veale Convocation Center, Cleveland, Ohio, Apr. 16-17, 2008.
    
    


MRI requires both transmitted radio frequency (RF) fields and received radio frequency (RF) fields. These RF fields are often denoted as B1 fields. The transmitted field, in typical usages, should be approximately uniform over the area being imaged within the subject. Spatial inhomogeneities of the RF fields introduce unwanted effects, including various artifacts in images, degradations in image contrast, or degradation or failure of various quantification methods. The transmit field acting within human bodies exhibits greater non-uniformity as main magnet field strength increases. The static magnetic main field is denoted as the B0 field. The effective B1 fields depend both upon the engineering design of the MRI scanner (such as RF antenna/coil geometry), and the geometry and electromagnetic properties of the subject within the scanner (often a human patient).
Having information about the distribution of non-homogeneity in the transmit B1 field within a specific subject can be beneficial in various ways. Advantages of having such data include being able to better interpret images and artifacts, being able to spatially improve the actual field patterns by improved design of the scanner, being able to interactively or dynamically refine the fields on specific subjects and in specific scan areas, and being able to improve or correct the acquired data and/or resulting images. In some more advanced methods, such as “multichannel transmit” or “Transmit SENSE,” knowledge of non-uniform spatial field patterns is explicitly needed and explicitly used to accomplish goals of improved RF excitation and spatial localization.
Numerous methods exist or have been proposed for experimentally determining the B1 field. When the information is determined or presented in the form of a 2-D or 3-D spatial distribution, it is called a B1 map.
A pulse sequence can be repeated several times using successive amplitudes of RF excitation (i.e., nutation) pulses. The receive MR signal intensity is known to have a certain functional dependence on the effective B1 transmit amplitude, such as:

S(θ(x,y,z), x,y,z)=[ρ(x,y,z)]*sin(θ(x,y,z))3   [Equation 1]

θ(x,y,z)=RF_ampl_factor*(B1_spatial(x,y,z))   [Equation 2]

where:

    
    
        S is measured data (using a pulse sequence acquisition at the scanner for various RF_ampl_factor values), and the unknown value of B1_spatial (i.e., θ or B1_spatial) are the spatial distribution(s) to be determined;
        “S” denotes the MR signal intensity (the actual mathematical functional dependence is based upon the pulse sequence used);
        ρ is a signal strength factor such as the proton density, or a proton density times the receive coil sensitivity, or the like;
        RF_ampl_factor is an independently adjusted control factor (e.g., RF pulse amplitude and duration) in the pulse sequence;
        B1_spatial(x,y,z) is the form of a spatially dependent B1 associated with some reference value of the RF_ampl_factor; and
        θ has the meaning of the spatially dependent effective B1 field.
    
    


The specific “S” formulae given above happen to be suitable for a pulse sequence producing a single stimulated echo with complete T1/TR signal recovery, and minimal T1, T2 decay during the echo time, just as an example.
In general, one detects or measures S, from which one can determine θ, from which one can determine B1_spatial. In the literature, sometimes authors compute and report θ, and sometimes they compute and report B1. Converting from one to the other is simple, and the two terms may be used somewhat interchangeably throughout the following description.
To be rigorous, B1_spatial should represent an instantaneous physical measurement of a component of a time-varying magnetic field. θ is the time integral of (γB1), and γ is a gyromagnetic ratio. The time integral can be a simple linear approximation or, more accurately, it can be the result of integrating out the full Bloch equations. These relationships are well known in MRI, and are not discussed further here. Suffice it to say, conversion between B1 and θ is straight-forward under typical imaging conditions.
Multiple measurements are generally needed, so that from multiple values of S, it is possible to solve for “ρ” and θ.
Spatially localized images can be collected at a series of amplitudes. Analysis such as searching for a peak, or fitting a curve, can be done to determine the strength of B1. In a simple exemplary case, such as a stimulated echo sequence where S=S(θ)=sin(θ)3, if we assume an approximately uniform B1_spatial(x,y,z), MR data can be collected at each of several RF_ampl_factor values over some nominal range. The RF_ampl_factor which yields the peak of the signal value “S” corresponds to θ(x,y,z)=π/2 (flip angle in radians), i.e., at the particular RF_ampl_factor for which S achieves a maximum, B1_spatial=(π/2)/RF_ampl_factor (once again, ignoring other factors such as γ, the RF pulse duration, etc.).
Other pulse sequences can be used, and other features of the signal strength function can be used, such as the first minimum of the signal for a 180° excitation pulse sequence, or such as the most-negative-valued signal for a 180° inversion pulse followed by a sign-sensitive readout.
The successive amplitudes can be controlled by stepping through a range in a prescribed fashion, perhaps linear increments across some nominal range, or by iterative search methods like bisection, etc.
The varying amplitude factor, RF_ampl_factor, can be altered and applied to all RF transmit pulses in a sequence in unison or, alternately, one or a few pulses can be modified, while others are kept constant. For example, in a spin echo pulse sequence with two nutation pulses (α1 and α2), the signal strength can have the form:

S(α1, α2)=sin(α1)*(sin(0.50 α2))2,

in which case α1 and α2 may be varied together, or either one can be varied independently.

When B1_spatial(x,y,z) is not treated as constant (i.e., spatially homogeneous), a simple but slow technique is to acquire and generate entire 2-D or 3-D images for each of several RF gain factors, and then to analyze the sets of images pixel-by-pixel, to fit or search for an amplitude scaling at each pixel location. Note that while using search algorithms and data-dependent choice of RF_ampl_factor to try to converge to some optimal condition may be a good strategy when B1 is spatially uniform, it is not as suitable when B1 is non-uniform. A value of RF_ampl_factor which achieves a goal such as a signal null at one location will not simultaneously achieve nulls at other locations, for example.
The resulting B1 strengths, or flip angles θ, are then collected and presented or stored in the form of an image, known as a B1 map. It is possible that the B1 value can be treated either as a magnitude or as a complex value which also includes some phase value (relative to a suitable or arbitrary reference phase).
Many acquisition methods are known which can be used to determine B1. Basically, all MRI pulse sequences have dependencies on B1 transmit fields, but some have more favorable characteristics, such as nearly linear dependencies over a range of transmit values, or such as dependencies which are uncoupled from other variables like the tissue T1 and T2 parameters. Corresponding analysis methods also exist, often for specific acquisition methods.
In some cases, a series of many RF pulse amplitudes are used in successive acquisitions. A feature such as a null or minimum in the signal level can then indicate which RF pulse amplitude is the nearest match to a certain flip angle or a certain B1 strength, as previously explained.
Determining θ from S may be done in any of a few ways. There can be some regression or fitting to yield both ρ and S (even though there may be no explicit interest in ρ). There could be a simple search for a simple feature of the signal curve such as a maximum or null. There are ways to collect a few values of S, (perhaps something like S1 using RF_ampl_factor=RF_amp_factor1, and S2 using RF_ampl_factor=(2*RF_ampl_factor1), then finding a closed form mathematical dependence of θ on S1 and S2, especially where that closed-form dependence has eliminated other variables like ρ.
It is common to collect pairs of images acquired with different numbers of RF pulses, or different amplitudes, and then form ratios of the images. The ratios cancel other factors contributing to image intensity, leaving terms which depend on the RF pulses. The signal ratios have dependencies upon the RF pulse amplitudes which can be computed and inverted.
We have previously described collecting data with a few values of RF_ampl_factor, each using the same pulse sequence and the same acquisition parameters (other than RF_ampl_factor). A variant of this idea, is to acquire instead two (or more) pulse sequences, two or more echoes, or the like. In one example, the two basic pulse sequences could be different, and each has a different functional dependence of S on θ (e.g., one spin echo with a saturation or inversion pre-pulse, and a second spin echo without the pre-pulse). In another example, two or more echoes can be acquired in a single, more complicated, pulse sequence (e.g., a spin echo and a stimulated echo, or some kind of first RF echo and second RF echo). In yet another example, a pulse sequence can be run with two sets of parameters, such as a short TR and a long TR, perhaps in an interleaved fashion.
One commonly referenced method which is an example of such a ratio calculation is the double angle method. (Insko, 1993; Stollberger, 1996, etc.)
It is known that RF tagging techniques (including “SPAMM”) depend upon RF amplitudes, and so they can be used for determining B1 spatial dependencies (B1 maps). (Axel, 1989, two references.)
In SPAMM RF tagging, two or more similar RF tagging nutation pulses are applied, and a pulsed gradient is applied in between them. The gradient causes spatial “modulation patterns.” One simple pattern is a periodic set of parallel stripes, with each cycle showing a generally sinusoidal intensity pattern. A simple physical explanation is that the two RF pulses can have similar effects individually, but the gradient applied after the first pulse causes a spatially dependent phase factor associated with the first RF tagging pulse. Then, depending upon this phase factor, the two RF tagging pulses may “add constructively” or “cancel each other like a destructive interference.” Thus, a series of stripes is generated, with bright untagged signal appearing at locations where the tagging pulses cancel each other, and with tagged reduced (dark) signal bands appearing in locations where the effects of the two RF tagging pulses combine together constructively. A mathematical description of this is given in Bernstein, King and Zhao, pages 166-171, 2004.
Bernstein at page 176 has a cursory reference to the fact that SPAMM pre-pulses can be used to figure out B1 maps. There are also some similar cursory references in one or both of the original Axel papers. While such references say it can be done, the inventors are not aware of anyone really doing it or publishing results until they did a version at the ISMRM Toronto May 2008 conference—and that was with purely image-based processing. When considering prior art use of SPAMM to achieve B1 mapping, it appears that there is limited published material.
The Axel papers allude to the fact that spatial tagging lines may appear as pairs of minima under certain conditions, and that the spatial separation of the pair of minima could be used to determine B1. The conditions for favorable application of this acquisition method and analysis approach can include a total tagging excitation higher than 90° (perhaps between 110° and 270°), magnitude image reconstruction, and image pixel resolution of multiple pixels across each full spatial cycle of the complicated tagging pattern.
Suppose the two pulses each have some nominal amplitude at a particular location, each yielding (perhaps) 35° tip angle in some region. The tagging portion of the acquisition sequence can then be described as having a total tagging RF nutation angle of 70°, which dictates the percentage of signal suppression at a trough in that region.
The prior Dannels, Chen and Shou approach using SPAMM-tagging for the acquisition (but a different analysis concept from that now to be described below) prefers a different set of favorable acquisition conditions. When the total tagging RF angle is less than about 90°, then the relative darkness of tagged areas can be used directly to determine the tagging RF angle. The resultant image has a structure of alternating bands or stripes, with both tagged and untagged signal. Bright peaks are untagged, and the darkest part of each trough corresponds to a location which is affected by the total tagging RF pulse's total B1 angle. Under such conditions, the ratio of a peak to a trough can then be sufficient to determine the effective B1 field. With such a strategy, the peak and trough are acquired totally simultaneously, in a single image. Thus, there should be minimal concerns about the sources of inconsistencies which exist between two or more measurements. (Patient motion is the most notorious source of these inconsistencies.) This is an intrinsic advantage of using the tagged image. In exchange for getting away from the data-consistency problem of using two or more acquisitions, the tagging method will, however, depend upon other consistency concerns across two or more locations. For example, the signal strength ratio is attributed to an RF tagging pulse (difference between a peak and a trough) and its local B1 field, so there should not be other major sources of deviation in “S”, such as confounding differences due to “ρ” or T1 or T2.
In an abstract submitted in November 2007 to the ISMRM conference of May 2008, one of the inventors (plus co-authors Chen and Shou) presented analysis of a method of detecting nearby peaks and valleys in an image with tagging, to compute the effective RF pulse amplitude which created the tag. The inventors consider this to be not a particularly effective method. (See “Feasibility of Rapid B1 Mapping with RF Prepulse Tagging,” X. Chen, X. Shou, W. Dannels, Proceedings of ISMRM 16th Scientific Meeting, Toronto, Canada, May 2008 abstract #3045.) Also documenting this approach is a poster which analyzes use of the same tagging acquisition, but using the (image-domain) processing of peaks and valleys. This poster was presented at Case Western Reserve University in April 2008.
Many of such prior techniques for B1 mapping have limitations of acquisition speed. For example, one minute for a 2-D map, or four minutes for a 3-D volume map, have been touted as being “fast” B1 mapping techniques. Motion artifacts in the body can degrade individual images, but more importantly, they can cause inconsistencies between pairs of images. Inaccuracies and biases can arise. Effects from T1 decay have been often analyzed. Techniques may require additional corrections or calibration (e.g., double angle is known to have a confounding effect, where selective excitation slice thickness and profiles exhibit an undesired dependence upon the local B1). (See Wang, 2006.) Arrival of signal level to equilibrium or steady state values can be slow, e.g., on the order of a few times T1. This can limit scan time or limit temporal resolution, or introduce errors in the presence of attempted faster acquisitions. Intrinsic SNR can adversely affect accuracy, resolution or scan acquisition time. There can be a limited dynamic range with respect to the deviation of B1 relative to a known nominal value. (See, for example, Dowell, 2007.) The associated acquisition technique for reading out the image may have limitations or artifacts, which would propagate into the associated maps. For example, EPI, as used in Jiru, 2006, can have significant geometric distortion, or chemical shift, or utilizes fat suppression, making it impractical to determine the B1 within fat.
Most of the prior techniques require longer acquisitions, costing several minutes of scanning for 2-D or 3-D maps. In many of these techniques, the different acquired images depend on not only RF pulse amplitudes, but also other factors such as T1, T2, or resonance frequency shifts, etc. This becomes a source of error in the resulting B1 determination, or else requires additional acquisitions to simultaneously determine both B1 and the other factors. When scans are longer, or more than one scan must be combined, physiological motion can degrade the individual acquired images, or make the separate images become inconsistent, ruining the ratios. Motion artifact can make techniques useless in human torsos. Using single tagged images avoids these problems, but requires more sophisticated processing. Detection of local signal variations in a tagged image, when the unmodulated image itself contains significant local variation, is not easy, especially when working in the image domain.
If the SPAMM acquisition is used with image-domain peak-and trough detection method, significant error can arise if a neighboring peak and trough are used together in a ratio, but they have other confounding effects, like major differences in ρ.
BRIEF SUMMARY
This application describes an improved way to determine spatial patterns and amplitudes of transmit RF fields in MRI systems. When used in conjunction with suitable MRI acquisition pulse sequences, measurements of patterns are produced which will depend both upon the design of the scanner and upon the subject. Thus, experimental measurement and determination on individual patients is more suitable than, say, theoretical calculations for a single patient or single geometric model. The technique can be especially advantageous at higher field strengths, in bodies and abdomens, or in cases where acquisition speed is important, or where motion in the body can make measurement problematic.
The current application describes a method for determining or calculating B1 maps, from experimentally acquired MR data of a suitable kind. In particular, advantages can be realized in accuracy or practical performance or speed when generating B1 maps, especially inside humans or moving, living subjects.
Sometimes transmit fields are denoted by Tx, or Tx B1, or the like, and because they can exhibit a certain polarity of circular polarization, they can also be denoted as B1+. Similarly, receive RF fields associated with samples and coils can be denoted as Rx, or Rx B1, or B1−, etc.
The exemplary embodiments to be described below generate a B1 map of RF B1 signal magnitude values in a MRI system by using an MRI system to:

    
    
        acquire at least one two-dimensional set of B1 amplitude-tagged MRI data signals in spatial frequency domain k-space from MR nuclei within an imaged volume of the MRI system;
        process such k-space data to produce at least two of three sub-sets of frequency-filtered k-space data (e.g., a baseline low frequency sub-set, and at least one of (a) a higher positive-frequency sub-set and (b) a higher negative-frequency sub-set, such higher frequency sub-sets including respectively corresponding harmonic versions of the baseline sub-set);
        separately transforming each of these at least two filtered sub-sets to respectively corresponding spatial domain data sets (e.g., a baseline magnitude set, and at least one of (a) a positive harmonic magnitude set and (b) a negative harmonic magnitude set);
        arithmetically combining the baseline magnitude set with the harmonic magnitude sets on a pixel-by-pixel basis to provide upper and lower magnitude envelope data sets;
        processing the upper and lower magnitude envelope data set values on a pixel-by-pixel basis to generate a B1 map data value based on an inverse function (e.g., trigonometric in the exemplary embodiments where sinusoidal tagging is used) of a value related to a ratio of the upper and lower pixel data values at a given pixel location in the spatial domain; and
        storing or displaying the B1 map data values for use in MRI system design and/or correcting/compensating diagnostic MR images taken by the MRI system (e.g., perhaps on a patient-by-patient basis).
    
    


Preferably, the acquisition of k-space data from MR nuclei is achieved by applying at least two RF excitation pulses with at least one interleaved magnetic gradient pulse in a pre-sequence before applying an MRI pulse sequence (e.g., one of the many conventional well known MRI pulse sequences) to elicit successive MR responses in the time domain which are then mapped to respectively corresponding positions of k-space (e.g., typically to provide successive, respectively corresponding, lines of a multi-dimensional set of k-space data in a spatial frequency domain.)
There are also advantages to be had if the original k-space data set is (a) two-dimensionally Fourier transformed to the spatial domain, and (b) further two-dimensionally Fourier transformed back to the spatial frequency domain k-space before further processing. This detour to the spatial domain and back again to k-space has been discovered to provide advantages in that it may produce a more idealized k-space data set for B1 mapping purposes. For example, if the MRI system happens to use multiple receiver coils with outputs that are combined to achieve complete data acquisition and/or uses parallel imaging techniques and/or uses complex-conjugate filling of a part of a k-space, etc., then experience has shown that a more idealized “starting” k-space data set (for B1 mapping) results from detouring into the spatial domain and back again into the spatial frequency domain.
The spatial-tagging pre-pulse sequence may also be of many different types. For example, there are well known tagging sequences such as the SPAMM (spatial modulation of magnetization) sequence and/or the DANTE (delays alternating with nutation for tailored excitation) sequence. Such tagging sequences can produce sinusoidally varying spatial modulation which permits trigonometric inverse functions to be used as in the exemplary embodiments. Other tagging sequences may produce non-sinusoidal modulation, thus necessitating use of alternate inverse functions.
The acquisition of a “starting” k-space data set may also involve multiple data acquisition cycles and combining of the resulting k-space data. For example, it has been found particularly suitable to acquire a first set of k-space data using a first tagging pre-sequence of at least two RF excitation pulses having the same sense of nutation angle and then also acquiring a second set of k-space data using a second tagging sequence of at least two RF excitation pulses having different, alternating nutation angle senses. The two sets of thus acquired k-space data are then arithmetically combined to produce a combined set of k-space data to be used as a “starting” k-space data set in subsequent steps of an exemplary embodiment. As will be explained in more detail below, this multiple acquisition and combination of k-space data can itself result in favorable reduction of harmonic content for the “starting” k-space data set to be used thereafter in an exemplary B1 mapping process.
Once a suitable “starting” k-space data set has been acquired (which may be a single first-acquisition k-space data set without detours or further preliminary processing), then it is spatial frequency-filtered in k-space by extracting k-space data from different portions of the k-space spatial frequency data set. In particular, the baseline low frequency sub-set of k-space is extracted, as well as at least one higher frequency harmonic-containing portion of k-space data (e.g., extracted from two other adjoining areas of k-space such as a strip of k-space located above the baseline strip and a strip of data located below the baseline in k-space). The extraction may be made with respect to strips or rectangular/square (or other shaped) windows in k-space (possibly having sharp or weight-shaped edges) so as to, in effect, perform a frequency-filtering function since the k-space data is already in the spatial frequency domain.
The frequency-filtered k-space extract data is then two-dimensionally Fourier transformed so as to bring it to the spatial domain—thus providing at least two sets of spatial domain data—where by using only magnitude values for each data point, one can effectively de-modulate the harmonic higher frequency data and be left with “envelope”-defining sets of values—one representing a low-frequency component and one representing higher frequency, demodulated components (e.g., located above (and/or below) the baseline component in k-space).
If the magnitude values from all sets of resulting spatial domain data are added on a pixel-by-pixel basis, this provides a map of the peak or “upper” signal magnitude envelope. Similarly, subtracting from the baseline magnitude set, on a pixel-by-pixel basis, the harmonic magnitude set(s) provides a map of trough or “lower” signal magnitude envelope values.
Once such minimum and maximum pixel values have been determined, then a “tag depth” ratio data set may be created on a pixel-by-pixel basis where, for example, each pixel of tag depth ratio data TD=min/max where min is the lower magnitude data set value and max is the upper magnitude data set value. One may then calculate the arccos of the tag depth ratio values (cos−1 TD) on a pixel-by-pixel basis so as to provide a B1 map of effective tag nutation flip angles θ. Of course, once the effective nutation flip angles θ are known, then the corresponding B1 magnetic field strengths may be calculated based on known formulae to provide a B1 map of effective B1 magnetic field strengths. Either the B1 map of effective nutation flip angles θ or the B1 map of effective field strengths B1 may, of course, be normalized by ratioing such values with the nominal desired value of θ or B1 provide a map of normalized B1 field strengths and/or flip angles θ.
Any of these types of B1 maps may, of course, be displayed on a screen or printer for visual observation/use (e.g., in designing MRI system changes and/or quantifying MRI images, “correcting” or “compensating” such MRI images, etc.).
Some advantages of this exemplary embodiment are:

    
    
        Compared to image-domain detection of peaks and troughs with tagged data, the exemplary processes reduce or remove errors from unequal baseline signals being used within a single ratio, and in a single determination of B1 in a region.
        The exemplary processes remove the need to locally fit to determine the actual height of a peak, (or the actual minima of a trough) when the location of the peak (or trough) is not centered on a pixel. If uncorrected, this would normally lead to underestimation of the signal level difference between peaks and troughs and, therefore, would lead to a bias towards underestimating the B1 level and the flip angle θ.
        The exemplary processes remove the bias which could arise when there is partial averaging of the tagging waveform within a pixel of finite extent.
        The exemplary processes are amenable to true single-shot readout, as a way to get rid of inconsistencies from human motion (e.g., temporal resolution of much less than 100 msecs can be obtained).
        The exemplary processes can be easily used in a breathhold, to gain immunity against respiratory motion artifacts.
        Since the main acquisition method can be changed to use various pulse sequences, there can be a wide range of resolution and sensitivity to MRI parameters, i.e., it is possible to choose a sequence with higher spatial resolution, or better sensitivity, or reduced sensitivity to motion.
        The exemplary processes can be used in the presence of diverse tissue types, including fat.
        The exemplary processes can be fully automated, and do not require secondary inputs such as T1 maps, or off resonance maps, or estimates of T2 or T2*.
        The exemplary processes have high dynamic range, even without extending the usable signal analysis range beyond 90° total tagging angle. For example, one acquisition can capture a range of flip angles from 20° to 80°, i.e., a dynamic range of 4-to-1.
        The exemplary processes have high immunity to noisy images, as a result of good filtering.
        The exemplary processes have the ability to get good spatial resolution, if desired (maps of 32×32 or less are not unusual with some other methods).
        The exemplary processes allow higher resolution, in terms of tag lines being potentially closer together, than in image-domain-based analysis of the tag lines. Note that the filtering step, or the step of generating an envelope of the modulation part, will generally introduce a blurring or loss of resolution in the B1 map, which is on the order of the spacing of the tag lines. Thus, closer tag line spacing, such as two, three or four pixels per cycle, as opposed to, say, 5-10 pixels per cycle, can yield a higher resolution B1 map.
    
    





BRIEF DESCRIPTION OF THE DRAWINGS
These and other objects and advantages of the exemplary embodiments will be apparent from the following more detailed description taken in conjunction with the accompanying drawings, in which:
FIG. 1 is a general overall schematic depiction of an MRI system configured to practice the exemplary embodiments;
FIG. 2 is a schematic depiction of a pre-sequence to be employed in conjunction with a following MR imaging sequence so as to acquire spatially-tagged k-space data for use in the exemplary embodiments;
FIG. 3 is a schematic diagram, at a relatively high level, of exemplary processes utilized in the exemplary embodiments for B1 mapping in an MRI system using k-space spatial frequency domain filtering;
FIG. 4 is a more detailed schematic flowchart of process control program code structure that may be utilized in an exemplary embodiment of the MRI system shown in FIG. 1;
FIG. 5 is a schematic diagram of k-space filtering utilized in an alternative embodiment;
FIG. 6 is also a schematic diagram of k-space frequency filtering utilized in an alternate embodiment;
FIG. 7 is a schematic diagram of an embodiment utilizing first and second data acquisition cycles with different tagging pre-pulse sequences followed by combination of the resulting k-space data sets so as to produce an improved “starting” k-space data set;
FIG. 8 is an image of a human pelvis with visible spatial modulation tagging lines superimposed thereon from use of a pre-pulse tagging sequence;
FIG. 9 is a B1 map generated from the tagged image of FIG. 8; and
FIG. 10 is a normalized B1 map from FIG. 9 with superimposed contour lines depicting variations in B1 effective magnitude across the human pelvis.



DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS
The MRI system shown in FIG. 1 includes a gantry 10 (shown in schematic cross-section) and various related system components 20 interfaced therewith. At least the gantry 10 is typically located in a shielded room. One MRI system geometry depicted in FIG. 1 includes a substantially coaxial cylindrical arrangement of the static field B0 magnet 12, a Gx, Gy and Gz gradient coil set 14 and an RF coil assembly 16. Along the horizontal axis of this cylindrical array of elements is an imaging volume 18 shown as substantially encompassing the head of a patient 9 supported by a patient table 11.
An MRI system controller 22 has input/output ports connected to display 24, keyboard 26 and printer 28. As will be appreciated, the display 24 may be of the touch-screen variety so that it provides control inputs as well.
The MRI system controller 22 interfaces with MRI sequence controller 30 which, in turn, controls the Gx, Gy and Gz gradient coil drivers 32, as well as the RF transmitter 34 and the transmit/receive switch 36 (if the same RF coil is used for both transmission and reception). The MRI sequence controller 30 includes suitable program code structure 38 for implementing a spatial-modulation pre-sequence (e.g., SPAMM or DANTE) in conjunction with other (e.g., conventional) MRI sequences already available in the repertoire of the MRI sequence controller 30.
The MRI system 20 includes an RF receiver 40 providing input to data processor 42 so as to create processed image data to display 24. The MRI data processor 42 is also configured for access to a B1 map program code structure 44 and to a B1 map memory 46 (e.g., for storing B1 map data derived from processing in accordance with the exemplary embodiments and the B1 map program code structure 44).
Also illustrated in FIG. 1 is a generalized depiction of an MRI system program store 50 where stored program code structures (e.g., for B1 mapping based on spatial frequency domain analysis) are stored in computer-readable storage media accessible to the various data processing components of the MRI system. As those in the art will appreciate, the program store 50 may be segmented and directly connected, at least in part, to different ones of the system 20 processing computers having most immediate need for such stored program code structures in their normal operation (i.e., rather than being commonly stored and connected directly to the MRI system controller 22).
Indeed, as those in the art will appreciate, the FIG. 1 depiction is a very high level simplified diagram of a typical MRI system with some modifications so as to practice exemplary embodiments to be described hereinbelow. The system components can be divided into different logical collections of “boxes” and typically comprise numerous digital signal processors (DSP), microprocessors, special purpose processing circuits (e.g., for fast A/D conversions, fast Fourier transforming, array processing, etc.). Each of those processors is typically a clocked “state machine” wherein the physical data processing circuits progress from one physical state to another upon the occurrence of each clock cycle (or predetermined number of clock cycles).
Not only does the physical state of processing circuits (e.g., CPUs, registers, buffers, arithmetic units, etc.) progressively change from one clock cycle to another during the course of operation, the physical state of associated data storage media (e.g., bit storage sites in magnetic storage media) is transformed from one state to another during operation of such a system. For example, at the conclusion of a B1 mapping process, an array of computer-readable accessible data value storage sites in physical storage media will be transformed from some prior state (e.g., all uniform “zero” values or all “one” values) to a new state wherein the physical states at the physical sites of such an array vary between minimum and maximum values to represent real world physical events and conditions (e.g., the sensitivity map for an RF antenna/coil over an imaging volume space). As those in the art will appreciate, such arrays of stored data values represent and also constitute a physical structure—as does a particular structure of computer control program codes which, when sequentially loaded into instruction registers and executed by one or more CPUs of the MRI system 20, cause a particular sequence of operational states to occur and be transitioned through within the MRI system.
The exemplary embodiments described below are superior ways to process acquisitions and compute B1 maps from images which have intensity modulation from tagging pulses.
The acquired single image has a spatial modulation imposed on it. The spatial frequency of the modulation is known. The amplitude of the modulation depends upon the strength of RF pulses and hence the spatial B1 (transmit field) dependency. Raw MR data (k-space data) for these scans includes a central section which generates the unmodulated (i.e., low-frequency base band) part of the image.
In a preferred embodiment, the k-space data is reconstructed to an image in the spatial domain in the usual way, including an (inverse) 2DFT and taking magnitude of the complex image. A further (forward) 2DFT is then used to convert it back to the k-space spatial frequency domain which contains shifted replicas which generate the higher frequency modulated components of the image. Simple windowing operations separate the modulated and unmodulated components (in k-space). The k-space data includes a “low-pass” unmodulated part of the signal, a “high-pass” modulated part with a positive spatial frequency, and a “high-pass” modulated part with a negative spatial frequency. Each of the parts (the two modulated parts and the unmodulated part) are then independently transformed back to the image domain. Taking magnitude (in the image domain) of complex quantities demodulates the modulated parts. One might choose to call these contributions “modulated-unmodulated” parts. Sums and differences of those parts, in turn, give robust maps of the maximal signal envelope and minimal signal envelope. The unmodulated part plus the modulated-unmodulated parts gives the peak envelope. The unmodulated part, minus the modulated-unmodulated parts gives the trough envelope. These generated envelopes are more accurate than quantifying peaks and valleys in the image domain. The technique is fast enough to be acceptable for calibrations or pre-scans, if needed, in clinical scanning applications.
The filtering in k-space can be done by multiplying the data by, for example, two, three (or more) window functions. A first window, for the low pass, can be positioned over the center of k-space, i.e., the D.C. component. Alternately, it is feasible to search the k-space data to detect the location with the highest peak, and to use that as the center for the low-pass window.
The locations at which to apply the at least one high-pass window (e.g., two in this exemplary embodiment, one for positive and one for negative spatial frequencies, respectively) can be determined in any of a few ways. The area of the gradient pulse used between the two RF tagging pulses can be multiplied by a Larmor frequency, to give a k-space distance, in units such as cycles per centimeter. This distance, plus knowledge of the imaging field of view, can be used to determine a distance in terms of a number of samples (presuming for example, critical Nyquist sampling rates). As an example, if the gradient area resulted in a cycle of accumulated phase every 6 millimeters, and if the imaging field-of-view were 24 centimeters, then the modulation amounts to 40 cycles of modulation across the image. Thus, by the Fourier shift principle, the modulated parts will be displaced by 40 samples to either side of the unmodulated low-pass central data. Therefore, one may multiply one copy of the k-space data by a window shifted 40 indices to one direction, and multiply another copy of the k-space data by an identical window shape, but displaced 40 indices in the opposite direction from the center. The particular window functions any of a wide set of shapes, such as Hanning, Hamming, Gaussian, Kaiser-Blackman, Fermi functions, etc., as are well known in signal processing and in MRI. An alternative to calculating the shift from gradient and sequence parameters is to search the k-space data to detect the location of these secondary peaks.
The windowing operations in k-space provide a kind of filtering and reduce noise, allowing better determination of peak and trough signal. But a more significant advantage arises from the fact that the unmodulated-modulated image-domain data and the low-pass unmodulated data now have their minor oscillations removed, and have meaningful values at all pixels. Areas with no signal will have values near zero. Thus, it is possible to form a ratio of two components at the same pixel. At a pixel which previously would have been a trough, there is now what amounts to an interpolated or fitted value which gives a reasonable estimated value of a peak at the same location. At a pixel which previously would have only been a peak, there is likewise an available estimate of a trough. And in between, there are high-quality fits to both peaks and troughs. Thus, the main source of error is removed, which used to arrive from changes in tissue signal as one moved from a peak location to a trough location. This greatly improves the quality of the B1 map in areas where the MRI tissue characteristics change.
On a pixel-by-pixel basis, the next step is to form a ratio of the minimal signal to the maximal signal. This ratio can be called the “tag depth” where a value approaching zero indicates near complete darkening (saturation) by the total tagging RF angle. The total tagging RF angle is then determined by taking the inverse cosine (arccos) or cos−1 of the tag depth TD=min/max. When the min is close to the max, TD is just less than one, and the tagging has minimal effect. When min is close to zero, then TD is also small which indicates the efficacy of the imposed tagging is close to 100% saturation.
Optionally, alternative measures might be generated for storage or display. For example, a “tagging efficiency” defined as (1−min/max) might be favorable for ease of human comprehension, as a value near 1.0 would then represent highly effective tagging saturation and 0.0 would be completely ineffective tagging.
The B1 field can be saved in any of a few representations. It is reasonable to express the value at each pixel as the magnetic field strength of the effective transmit RF field. Alternately, it is reasonable to show the flip angle of a particular pulse, or the total tagging RF pulse.
Another favorable representation of the B1 map is to form a ratio, giving the actual local value normalized by the nominal value specified in the sequence. This ratio could be formed between tip angles, or between B1 field strengths, etc. In such a representation, a value over 1.0 would indicate “over-tipping”; 1.0 is the ideal value, and values under 1.0 indicate under-tipping. Such a representation can be useful because it includes not just the spatial variation of the B1 Tx field, but it also captures any effects of calibration or system gain errors. It characterizes the entire MR system transmit RF, including possible deviations in calibration, transmitter gain, etc.
Within reason, the time from the tagging to the excitation pulse should be kept short, especially compared to the T1 values of the materials, to minimize a source of bias, where T1 relaxation of the tagged nuclei could cause their amplitude to be under-estimated, and the B1 value also underestimated. Similarly, the duration of each individual tagging pulse should be kept short, as otherwise off-resonance during a pulse can lead to different effective tip angles. In particular, off-resonance can introduce a bias, and underestimating of the RF pulse angle and the B1.
A typical data acquisition sequence is depicted at FIG. 2 where a SPAMM pre-sequence precedes a conventional MR imaging sequence. Here, in this particular example, two 30° RF nutation pulses are transmitted into the imaging volume and between them, a SPAMM magnetic gradient pulse is interleaved. The spatial modulating frequency will be proportional to the integral of the tagging gradient. An optional spoiler pulse may also be employed after the pre-sequence and before the conventional MR imaging sequence begins. As will be appreciated, the received RF signals occur later during the conventional MR imaging sequence. However, they will have been spatially modulated because of the pre-sequence depicted at FIG. 2. In the example of FIG. 2, the SPAMM spatial encoding (i.e., “tagging”) gradient pulse is imposed by using Gy (typically the phase encoding gradient in a conventional MR imaging sequence), although it could also be imposed via the Gx gradient (which is shown in parenthesis in FIG. 2). The optional spoiler pulse could be provided by any of Gx, Gy or Gz. Typically, Gz is used as the “slice-select” gradient during subsequent RF excitation pulses in a conventional MR imaging sequence, while Gx is applied during read-out of, for example, an RF echo response in the time domain so as to frequency encode the read-out RF signals in the x spatial dimension.
A high level schematic depiction of an exemplary process is provided at FIG. 3. Here, at 300, k-space MR image data is acquired with cosine-like spatial modulation (e.g., at a spatial frequency kf that is determined by the tagging gradient used during the pre-sequence as noted above).
As earlier indicated, some advantages can be had by twice two-dimensionally Fourier transforming the originally acquired k-space data so as to create a processed “starting” k-space data set before frequency filtering operations are performed in accordance with this embodiment.
As depicted on the right side of FIG. 3, one row of k-spaced data in the spatial domain will have superimposed modulation at a spatial frequency kf.
The “starting” k-space data set is then frequency filtered at 310, 320 and converted to the spatial domain (e.g., by 2DFT). The filter bank 310 is a low-pass filter providing magnitude output L, while the filter bank 320 is a high-passband filter with passbands located above and below the low-pass filter bank at +−kf. The filtered higher passband spatial domain data sets (e.g., based on harmonics of the base band signal) are then demodulated at 330 (e.g., by taking absolute values of complex values) to provide a pair of higher frequency envelopes +E and −E. Rough schematic depictions of an exemplary one row of data across the image in the spatial domain are depicted to the right in FIG. 3 for reach of these outputs.
At 340, a smoothed “upper” curve (L+E) is derived, while at 350, a smoothed “lower” curve (L-E) is derived. Once again, a depiction of one row of data cross the image in the spatial domain is shown to the right side of FIG. 3.
At 360, a “tagging depth” ratio R can be calculated at each pixel by taking a ratio between the “lower” and “upper” data magnitude values. This ratio can then be converted at 370 to an effective nutation RF pulse angle θ (which is proportional to B1 magnetic field strength) by using an inverse trigonometric function. For example, the quantity L/U can be used in conjunction with the arccos function so as to compute θ. Of course, as will be appreciated, θ can be converted to B1 magnetic field strength and either or both θ, B1 values can be normalized with respect to the nominal expected control values used for the original pre-pulse nutation modulation.
Finally, at 380, the resulting θ, B1 map data can be displayed, stored in machine-readable accessible storage media, or otherwise used (e.g., by retrieving it from storage data) to compensate a diagnostic image—perhaps for the very same patient anatomy that was in place during the derivation of the B1 map data.
A more detailed program code structure is depicted at FIG. 4 for the MRI system of FIG. 1. Here, if a B1 mapping process is chosen, the process is initiated at 400. Thereafter, at least one set of k-space data tagged with spatial modulation is acquired at 402. For example, it may be acquired with a known spatial modulation frequency fm. Although various sizes of k-space data arrays may be used (e.g., 32×32, 64×64, 128×128, etc.), for a hypothetical example, it may be assumed that fm is equal to one cycle every 2 cm or 0.5 cm−1. Let it also be assumed that the k-space array is a 128×128 point array covering a square 256 mm slice of the imaging volume. This equates to an approximately 0.2 cm per pixel resolution, meaning that there are about five lines of spatial modulation per centimeter, and a total distance of about 12.8 k-space data points between harmonics of the base band signal appearing at the origin of k-space (i.e., kx=0 and ky=0 at the center of k-space). In this example, then a base band strip of k-space approximately twelve lines wide and centered upon the middle “zero” line would constitute the baseline low frequency filtered portion of k-space. A similarly sized strip just above the baseline strip of about twelve lines wide would then constitute the high-pass “positive” filtered segment of k-space, while a similar twelve line segment or strip located just below the baseline across k-space would constitute the high-pass “negative” frequency filter passband.
As those in the art will appreciate, the variables could otherwise be chosen such that the entirety of k-space would simply be divided into thirds with the middle third being the base band low-pass frequency component and the upper and lower thirds being the positive and negative high-pass filtered components, respectively. When k-space is evenly divided in this manner, it facilitates the design of the transition bands of the high-pass and low-pass filters, as will be appreciated by those in the art.
If desired, at 404, a decision point may be inserted as to whether or not one wishes to compensate for MRI system variables by performing a first two-dimensional Fourier transform of the original k-space data at 406 into the spatial domain and then a second two-dimensional Fourier transforming from the spatial domain back to the frequency domain at 408 before arriving at a suitable “starting” k-space data set. Of course, as those in the art will appreciate, this may be done automatically all the time or never rather than to provide a user-controlled decision point 404.
The appropriate desired “starting” k-space data is then frequency filtered by dividing it into at least three portions (in this exemplary embodiment): a low-pass baseline part=LP, a high-pass positive modulated part=HP+ and a high-pass negative modulated part=HP−.
Each of the frequency filters (e.g., extracted parts) of k-space data are then two-dimensionally Fourier transformed so as to convert them back to the spatial domain—and demodulated by using only the magnitude of the spatial domain values at 412, 414 and 416, respectively.
Thereafter, on a pixel-by-pixel basis, all three of the filtered sub-sets are summed at 418 to provide a map of peak or maximum signal envelope values. At 420, a difference is taken between the low-pass baseline magnitude values and the sum of the high-pass side bands so as to provide a pixel-by-pixel map of the trough or minimum signal envelope values.
Thereafter, at 422, on a pixel-by-pixel basis, a tagged depth value is calculated which, in this exemplary embodiment designed for use ultimately with an arccos function, is calculated at min/max. As will be appreciated, at each pixel, this value then involves taking the ratio of the minimum to maximum values.
Thereafter, in this exemplary embodiment, at 424, the arccos of the tagged depth value is calculated for each pixel so as to derive an effective RF flip pulse angle θ for each pixel, thus providing a map of flip angle θ values. If desired, the θ values may be converted to B1 magnetic field strength values at 426 using well known formulae.
In addition, if desired, normalized θ and/or B1 map values can be generated at 428. Any or all of such θ, B1 map values are then stored and/or displayed and/or printed at 430 as may be desired. Such map values can also be used at 432 so as to compensate diagnostic images from the MRI system (perhaps from the very same patient that was used to generate the B1 maps) and/or to design improvements to the MRI system and the like, as will be appreciated by those in the art. Exit from this routine is taken at 434 and, as schematically depicted in FIG. 4, the program code structure may be configured with optional exits (or jumps to a desired type of mapping) at many desired points (e.g., at 436, 438, 440, 442 or 444).
Some enhancements (enumerated as 1-15E below) can provide optimizations of the acquisition pulse sequence, as ways to enhance the overall performance of B1 mapping. In narrow terms, the exemplary embodiment is mainly a processing and analysis process. But in broader terms, the overall method can be improved in some cases, by coupling the processing with an enhanced acquisition, and that acquisition enhancement may not have special significance outside its use with the exemplary embodiments desired herein.
Enhancement 1: Higher harmonic terms may be used to fit more complicated modulations. This can extend the dynamic range of RF tagging pulse amplitudes, beyond the sinusoidal patterns associated with magnitude image reconstruction and tags of less than 90° RF amplitude. Different tag line patterns are shown in the Bernstein, King and Zhou book. For example, to extend dynamic range of tagging pulses, one could characterize the tagging shape, by showing how the first two, three or four Fourier components of the modulation pattern are expected to vary with the total tag RF angle. Then, one can window and reconstruct multiple harmonics independently, and finally one can select the tagging angle which has the expected ratio of components which most closely match the data at a pixel.
Enhancement 2: The time shift between the component RF pulses inside SPAMM-like tagging pre-pulse can be constrained, so that the shift of the tag lines for the off-resonance difference between fat and water is substantially a multiple of the time period needed for one cycle of phase to accrue between these species. For example, at 3T, the tagging pre-pulse could be generated by two pulses, timed such that the delay from the center of one pulse to the center of the next pulse is about 2.3 milliseconds. This time increment is known in other MRI pulse sequences as a “fat-water in-phase echo time.” The reason to do such is so that the location of stripes in fat and stripes in water signal are the same, and fractional shifts of the RF tagging pattern are not encountered when crossing a fat-water interface. This makes the filtering and separation of the modulated component more robust.
Enhancement 3: If an echo train-based readout technique [EPI, FSE, FASE] is applied after the tagging, the effects of amplitude decay modulation of the echo train must be considered. The effect of the amplitude decay must be identical in each replicant. Otherwise, if different signal components were centered at different parts of the amplitude decay, then the different replicants would have different T2 decay, and their amplitudes could not be directly used in ratios, without error or biases. Therefore, the shift direction of the replicants should occur along the readout direction in k-space.
Enhancement 4: The filtering of the k-space data as described is along one direction. The resultant B1 map will have its spatial resolution limited in that direction. However, in the opposite direction within the image, higher spatial resolution may be obtained. Filtering can involve collecting and merging in two directions—one of which achieves good resolution near a horizontal edge direction, and the other of which achieves good resolution near a vertical edge direction.
Enhancement 5: If two excitations are desired without waiting for full recovery, this might be done by collecting them with different spacing tag orientation shifted 90° (or tag spacing shifted). While the first set of tags may not have fully recovered, that first set can be ignored if it falls outside the window (in k-space) which would be needed to filter and separate a second set of tags, and so on.
Enhancement 6A: Signed or complex image input may be utilized (i.e., not the usual magnitude reconstruction of complex signal). Then, the modulation range can exceed a 90° total tagging angle, for better dynamic range, while still using simple k-space filtering of the first sinusoidal harmonic in the tagging pattern.
Enhancement 6B: When the spatial domain images used are magnitude or real, as opposed to complex, then it is noted that the k-space data contains Hermitian symmetry. It is possible to take direct advantage of the fact that shift frequency bands at positive and negative frequencies are related by reflection about the center of k-space, and by complex conjugation. Thus, it is possible to perform alternate equivalent operations such as windowing only the positive shifted frequency band, performing a 2DFT on it, and then generate the equivalent shifted frequency results by taking the real part of the 2DFT result and multiplying it by 2. These variations derive from the basic mathematical properties of the Fourier transform, and are well known in the art.
Enhancement 6C: When the images used are complex, it is also possible to work with just one of the shifted frequency sidebands instead of both the positive and negative direction shifted frequencies. As one example, it is possible to use one sideband, either the positive frequency harmonic or the negative frequency harmonic, double its contribution, and not use the other shifted frequency sideband at all, while accepting some artifact or degradation in the resultant 2DFT spatial domain results. It is also possible to use known MRI reconstruction techniques for reconstruction of partial datasets, in a way which reduces the artifacts. For example, a low resolution phase map can be generated from the main low-pass frequency image, and this phase map can be used for correction when synthesizing an equivalent 2DFT spatial domain image corresponding to what would result from the negative sideband. These kinds of methods are well known in the MR literature, where they are commonly known as partial Fourier reconstructions, asymmetric k-space acquisitions, conjugate symmetry reconstructions, and the like.
Enhancement 7: At a major edge, such as the exterior of the body, there can be point-spread issues which differ between the high-pass and low-pass portions. This can lead to bad computed data for the flip angle or B1 in those areas. Similarly, this can occur near signal voids. One step in the processing can be to generate a mask to identify areas of very low signal, or very significant signal gradients, or both. Then an erosion operator may be used on the mask image, to remove edge regions in the B1 map, which may have larger error.
Enhancement 8: Besides the map of B1, a secondary map such as p can be generated, or a mask can be formed by thresholding of ρ, so that in subsequent operations using the B1 map, it is known for which pixels we have generated a reasonable estimate of B1, and for which pixels there is no such estimate available.
Enhancement 9: Relative amplitudes and/or relative phase of distinct RF transmit channels could be determined by an extension of this method. Consider a system with two transmit coils. The acquisition pulse sequence could be repeated two or three times. In a first repetition, a single transmit coil or channel could be used for both of the RF tagging pulses. In a second repetition, the two RF tagging pulses can be applied where one coil is used to transmit the first pulse of the tagging pair, and the second coil is used to transmit the second RF pulse of the tagging pair, in which phase-sensitive maps of the modulation (high-pass) components can be generated from each map.
Optionally, a third repetition can be performed in which the second coil is used for both pulses. From the basic phase difference of the two maps, one can compute the relative phase difference of the two transmit coils. Many different similar alternatives should be easy to conceive by one skilled in the art, such as extension to larger numbers of coils.
Enhancement 10: Tagging structures other than two-pulse SPAMM can be used (however, the sinusoidal modulation that arises from two-pulse SPAMM does correspond to a particularly easy case for filtering in k-space, and for demodulating). In particular, any pattern that has structure which is locally substantially periodic should be a candidate for filtering and separation in k-space.
Enhancement 11: The example diagram herein for processing shows the process beginning with magnitude images, then optionally performing a reverse transform to convert back to a k-space data representation. This can have certain practical advantages, such as implicitly allowing for use of auxiliary functions that are performed in a product reconstruction (combination of data from multiple receiver coils being one example). However, it is not necessary to convert to and from the image domain before filtering. An alternative is to directly apply window filtering and separation to the raw acquired k-space data, without first performing forward and backward transforms.
Enhancement 12A: Single-shot acquisition is a suitable choice for the imaging readout of this method (for example, single-shot EPI, or single-shot FSE, or as is available in Toshiba® MR application software, single-shot FASE). It is also reasonable, however, to use a multiple-shot imaging readout. If a multiple shot readout is used, then the preferred implementation is to allow the signal to recover from the tagging pulses, before re-applying the tag and collecting the next shot. For example, the recovery time could be in the range of three to four time constants of the typical range of T1 encountered in the tissues. This general advice would apply to any tagging analysis, and may not be specific to the k-space filtered analysis.
Enhancement 12B: If more than one shot is needed, or more than one image, then one can contemplate using a saturation and spoiling pulse directly after each imaging readout. This would enable faster readout, i.e., maybe somewhat faster than TR=T1, without leaving residual bias to the tag line intensities (the bias arising from unequal saturation and incomplete recovery). This general advice would apply to any tagging analysis, and may not be specific to the k-space filtered analysis.
Enhancement 13: When extending the technique from 2-D maps, to 3-D maps, 3DFT is a good choice if SNR is more limiting than motion. Alternately, sequential 2DFT acquisitions, separated by significant time for the tags to recover between each slice, is a good choice of an imaging readout sequence whenever control of patient motion is more critical than SNR. This general advice would apply to any tagging analysis, and may not be specific to the k-space filtered analysis.
Enhancement 14: If windowing of the central lobe and shifted replicants is done in one dimension, then increased energy from distant areas of k-space may appear in the wrong window. This may lead to artifacts, such as diagonal edges in the B1 map exhibiting a stair-stepping pattern or local superimposed “zebra stripes.” One simple way to reduce the relative error from signal being included in the wrong window is to apply a filter or window along the opposite direction in k-space. The result is a 2-D window or filter as depicted in FIG. 5.
Near the center of one replicant echo, for example, the power of the signal from the modulated signal part will greatly exceed the power of the other two parts (unmodulated part, and other replicated part with whose frequencies have the opposite sign). But at farther distances in k-space, the error signal from the other parts becomes comparable to, or possibly even greater than, the power from the correct modulated part. Thus, these more distant areas contribute relatively more error, and should have reduced weighting or should be completely windowed out of the individual processing of the individual components.
Another method to reduce error is simply to acquire fewer lines of k-space.
As depicted in FIG. 5, the main unmodulated base band signal 500 appears shifted to the left for a first “negative” harmonic at 502, and shifted equally to the right at 504 for the first harmonic modulated “positive” signal in k-space. The diagonally extending hash marks from each of the principle lobes (depicted by circled crosses or plus signs) can thus be seen to extend into the center window region at 506 from the upper and lower side bands or harmonics. Accordingly, to help diminish this unwanted effect, a 2-D window rather than complete strip of k-space can be employed at 508 so as to filter out at least some of the interfering ripples from adjacent side bands/harmonics. Similar 2-D windows (e.g., rectangular, square, circular, etc.) can be utilized for all three components of frequency filtering in k-space as depicted at 510 in FIG. 5.
Enhancement 15A: The distant k-space signal from one signal component (i.e., from the unmodulated-component, or from the modulated-positive-frequency-component, or from the modulated-negative-frequency-component) can appear inside the main filtering window of another component (as also mentioned in enhancement or alternate embodiment 14). This signal can be thought of as a kind of baseline ripple, upon which the correct signal component is added. If the baseline ripple can be reduced or removed, then the artifact will be reduced or removed. We now describe four technical ways to reduce or remove the “baseline” ripple.
Enhancement 15B: As depicted in FIG. 6, one can collect one tagged acquisition with the tags oriented in one direction (e.g., as in 602 with the tagging gradient along the X direction for a transversely oriented B1 map), and also collect a second tagged image, with the tags oriented along the opposite in-plane direction as in 604, that is along the Y direction. With the two acquisitions in the two directions, replicants will occur with data at four locations, i.e., +kx, −kx, +ky and −ky. Select the scan parameters, including, for example, the k-space echo order and the phase encoding direction, so that as much as possible within reason, the echo decay at the same locations in k-space is the same. When the tagged components are shifted along the (plus-or-minus) kX direction, save a copy of the baseline ripple as detected by the windows situated at the (plus or minus) ky-shifted locations at depicted at 606. When, in the other acquisition, the tagged components are shifted along the (plus-or-minus) kY direction, save a copy of the baseline ripple as detected by the windows situated at the (plus or minus) kx-shifted locations. Subtract a copy of the measured baseline ripple in each shifted window from the acquired modulated signal in that same window as shown at 610, 612, to at least partially reduce the baseline ripple. Combine the maps from the two corrected acquisitions.
If the sequence uses an echo train-based readout technique (EPI, FSE, FASE, etc.), multiple shots of segmented k-space should be used. Here, the choice of phase encode schedule per shot is important. The phase encode schedule dictates the amplitude decay modulation function. In the first acquisition (tag along X), by acquiring the readout direction along the same direction of the shift (±kx), the central low frequency component and outer high frequency components are centered within the same position of the amplitude decay modulation function. All components experience the same amplitude decay modulation. In the second acquisition (tag along Y), the phase encode direction must be the same as the first acquisition. Only the direction of the shift should change (to ±ky). The components must all be centered in the same positions of the phase encode schedule within each segment. The segment size, phase encode schedule and/or tag cycle spacing must be chosen accordingly. Therefore, for the technique of baseline removal, if using an echo train readout method, the number of shots (segments) might naturally be a multiple of 3. A separate shot can be used for each component in the second acquisition to ensure that the component is centered in the amplitude decay function the same way. In this way, the ripple estimate regions of interest (A, B, C, D in FIG. 6) and the shifted components are all affected by the same amplitude decay modulation function in the same way. Since the ripple estimate regions have the same amplitude decay modulation as their corresponding shifted components, a direct subtraction can be performed.
Enhancement 15C: As in 15A, collect data with two (or more) orientations of the tag data. Generate an uncorrected B1 map from each acquisition. Combine the images on a pixel-by pixel basis, such as by simple averaging, or by performing a weighted combination, with preferential weighting at each location in image space for the B1 map which has the least high-frequency content potentially interfering with the tagging modulation patterns of each tagging orientation.
Enhancement 15D: Collect one copy of the acquisition with tags, and one without tags. Note the location where filter windows are placed over the shifted signal components with modulated signal in k-space. From corresponding locations of windows over the untagged scanned k-space data, extract copies of the high frequency k-space data (these would be the baseline ripples). Optionally, determine an amplitude factor, showing how the central untagged component of the data has reduced overall amplitude in the k-space. Subtract the baseline ripple estimates (optionally multiplied by the factor for reduced amplitude). Proceed with the rest of the map generation process.
Enhancement 15E: Collect two acquisitions, each of which could be used to generate a B1 map. The first acquisition pre-pulse sequence shown in FIG. 7a is as previously described for FIG. 2. However, in the second acquisition at FIG. 7b, the sequence is modified so that the spatial locations of the peaks and troughs in the (sinusoidal) tagging pattern are reversed. This may be done by inverting the polarity or phase of one of the two RF tagging pulses. Suppose the first acquisition has a tagging sequence which is symbolically denoted as (+αRF, Gtag_encode, +αRF). Then the second acquisition can have a sequence which is symbolically denoted as (+αRF, Gtag_encode, −αRF).
Extract the three components from each of the two acquisitions (as shown, respectively, at FIGS. 7c and 7d in which these six components are labelled as LP+alpha, LP−alpha, HP+alpha+freq, HP−alpha+freq, HP+alpha−freq, HP−alpha−freq where the part of the label either “+alpha” or “−alpha” refers to which RF polarity is used in the two acquisitions. Then, form some combinations by additions and subtractions:

LP=(LP+alpha)+(LP−alpha)

HP+freq=(HP+alpha+freq)−(HP−alpha+freq)

HP−freq=(HP+alpha−freq)−(HP−alpha−freq)

where LP is the low-pass (or unmodulated) component, and HP+freq and HP=freq are components which are modulated (high-pass) and shifted to positive and negative frequency displacements.
This phase cycling scheme causes cancellation of the baseline ripple. Other variants of phases will be obvious to those skilled in the art, i.e., they are corrected so as to have the contribution from the unwanted signal removed.
Proceed with the rest of the map generation process.
FIGS. 8, 9 and 10 are photographs of a particular implementation of alternative 15E. Here, FIG. 8 shows the spatial domain image of a pelvis with the tagging lines shown. FIG. 9 is a normalized nutation angle θ map generated from the tagged image of FIG. 8. FIG. 10 shows the θ map of FIG. 9 with superimposed contour lines where 1.0 means measured total tip angle matches what was nominally specified, 0.80 means that the tip angles are 20% below that which was nominally specified, etc.
While only a few exemplary embodiments have been described in detail above, those skilled in the art will recognize many novel features and advantages of these embodiments may be realized even though many of the details are altered from the exemplary embodiments. All such modifications and variations are intended to be included within the scope of the appended claims.

## Claims

1. A method for generating a B1 map in an MRI system, said method comprising using an MRI system to:
(a) acquire at least one set of B1 amplitude tagged MRI data signals in spatial frequency domain k-space from MR nuclei within an imaged volume of the MRI system;
(b) process said k-space data to produce at least two sub-sets of frequency-filtered k-space data: (i) a baseline low-frequency sub-set, and (ii) at least one of a positive higher frequency sub-set including a harmonic version of said baseline sub-set and a negative higher frequency sub-set including a harmonic version of said baseline sub-set;
(c) separately transform each of said sub-sets to respectively corresponding spatial domain data sets: (i) a baseline magnitude set, and (ii) at least one of a positive harmonic magnitude set and a negative harmonic magnitude set;
(d) arithmetically combine said baseline magnitude set with said at least one of the harmonic magnitude sets on a pixel-by-pixel basis to provide upper and lower magnitude data sets;
(e) process said upper and lower magnitude data set values on a pixel-by-pixel basis to generate a B1 map value based on value related to a ratio of said upper and lower pixel data values at a given pixel location in the spatial domain; and
(f) store said B1 map of values in a computer accessible and readable memory device for subsequent use by said MRI system.

2. The method of claim 1, wherein step (a) comprises:
applying at least two RF excitation pulses with at least one interleaved magnetic gradient pulse pre-sequence before applying an MR imaging pulse sequence to elicit successive NMR responses in the time domain which are mapped to respectively corresponding portions of a two-dimensional set of k-space data in a spatial frequency domain.

3. The method of claim 2, wherein step (a) further comprises:
applying a 2DFT (two-dimensional Fourier transform) to an originally-acquired set of two-dimensional k-space data to provide a two-dimensional set of spatial domain data; and
applying a 2DFT to said two-dimensional set of spatial domain data to provide another two-dimensional set of k-space spatial frequency domain data for use in subsequent step (b).

4. The method of claim 2, wherein said pre-sequence is a SPAMM (spatial modulation of magnetization) sequence and step (e) uses an inverse cosine function of said ratio to generate B1 map values.

5. The method of claim 2, wherein said pre-sequence is a DANTE (delays alternating with nutations for tailored excitation) sequence.

6. The method of claim 1, wherein step (a) comprises:
acquiring a first set of k-space data using a first tagging pre-sequence of at least two RF excitation pulses having a same nutation angle sense;
acquiring a second set of k-space data using a second tagging sequence of at least two RF excitation pulses having different alternating nutation angle senses; and
arithmetically combining said first and second sets of k-space data on a pixel-by-pixel basis to produce a combined set of k-space data to be used in subsequent steps.

7. The method of claim 6, wherein step (a) further comprises:
applying a 2DFT (two-dimensional Fourier transform) to said combined set of two-dimensional k-space data to provide a further two-dimensional set of spatial domain data; and
applying a 2DFT to said further two-dimensional set of spatial domain data to provide yet another two-dimensional set of k-space spatial frequency domain data for use in subsequent step (b).

8. The method of claim 1, wherein step (b) comprises:
extracting k-space data from a mid-portion of k-space to produce said baseline low-frequency sub-set;
extracting k-space data from a different portion of k-space disposed to one side of said mid-portion to produce said positive higher frequency sub-set; and
extracting k-space data from another different portion of k-space disposed to another side of said mid-portion to produce said negative higher frequency sub-set.

9. The method of claim 8, wherein said extracting steps multiply respectively corresponding shaped window functions by k-space data.

10. The method of claim 8, wherein said extracting steps extract horizontal or vertical strips across k-space data.

11. The method of claim 8, wherein said extracting steps extract rectangular or square areas within k-space data.

12. The method of claim 1, wherein step (c) comprises:
separately applying a 2DFT to each of said sub-sets of frequency-filtered k-space data to convert such into the spatial domain and then using only the magnitude value for each resulting pixel data point to respectively provide said magnitude sets of spatial domain data.

13. The method of claim 1, wherein step (d) comprises:
adding all three magnitude sets of spatial domain data on a pixel-by-pixel basis to provide a map of peak or upper signal magnitude envelope data set; and
subtracting from the baseline magnitude set the sum of the harmonic magnitude sets on a pixel-by-pixel basis to provide a map of trough or lower signal magnitude envelope data set.

14. The method of claim 1, wherein step (e) comprises:
creating a tag depth ratio (TD) data set on a pixel-by-pixel basis where each pixel of the tag depth ratio data set corresponds to TD=min/max where min is the lower magnitude data set value and max is the upper magnitude data set value; and
calculating the arccos of TD on a pixel-by-pixel basis to provide a B1 map of effective tag nutation flip angles.

15. The method of claim 14, wherein step (e) further comprises:
calculating a normalized value for effective/intended tag nutation flip angles on a pixel-by-pixel basis to provide a B1 map of normalized tag nutation flip angles.

16. The method of claim 14, wherein step (e) further comprises:
calculating B1 strength based on said tag nutation flip angles on a pixel-by-pixel basis to provide a B1 map of effective B1 field strengths.

17. The method of claim 16, wherein step (e) further comprises:
calculating a normalized value for effective/intended B1 field strength on a pixel-by-pixel basis to provide a B map of normalized B1 field strengths.

18. The method of claim 1, further comprising:
(g) displaying, on a display screen or printer, said B1 map of data values for visual observation by a user of the MRI system.

19. The method of claim 1, further comprising:
(g) using said stored B1 map of data values to provide image compensation to a diagnostic image acquired by said MRI system, thereby providing a corrected diagnostic image of improved quality.

20. The method of claim 1, wherein step (b) processes said k-space data to produce more than three sub-sets of frequency filtered k-space data by including further sub-sets encompassing respectively associated higher harmonic components of the spatial modulation.

21. The method of claim 20, wherein determination of a B1 map value at each pixel includes a data fitting process using the associated higher harmonic components.

22. The method of claim 1, wherein step (a) comprises constraining the time shift between pre-sequence tagging RF pulses so that the shift of the tag lines for off-resonance difference between fat and water species nuclei is substantially a multiple of the time period needed for one cycle of phase to accrue between these species.

23. The method of claim 1, wherein step (a) utilizes plural RF transmit channels and an acquisition pulse sequence is repeated plural times using different ones or combinations of the RF transmit channels for respectively corresponding different acquisition pulse sequences.

24. A computer-readable storage medium containing computer program code which, when executed, effects the method of claim 1.

25. An MRI system comprising:
(a) an MRI scanner configured to acquire at least one set of B1 amplitude tagged MRI data signals in spatial frequency domain k-space from MR nuclei within an imaged volume of the MRI system;
at least one processor configured to:
(b) process said k-space data to produce at least two sub-sets of frequency-filtered k-space data: (i) a baseline low-frequency sub-set, and (ii) at least one of a positive higher frequency sub-set including a harmonic version of said baseline sub-set and a negative higher frequency sub-set including a harmonic version of said baseline sub-set;
separately transform each of said sub-sets to respectively corresponding spatial domain data sets: (i) a baseline magnitude set, and (ii) at least one of a positive harmonic magnitude set and a negative harmonic magnitude set;
arithmetically combine said baseline magnitude set with said at least one of the harmonic magnitude sets on a pixel-by-pixel basis to provide upper and lower magnitude data sets;
process said upper and lower magnitude data set values on a pixel-by-pixel basis to generate a B1 map value based on a value related to a ratio of said upper and lower pixel data values at a given pixel location in the spatial domain; and
(c) a data memory configured to store said B1 map of values in a computer accessible and readable memory device for subsequent use by said MRI system.