Abstract:
Metabolite images are produced with an MRI system using a priori information about the resonant peaks of the metabolites and their relative sizes to reduce the amount of NMR data needed for proper spectral resolution. With the a priori information the acquired NMR signal is modeled. Using this model and NMR data acquired at a plurality of echo times (TE), the metabolite at each image pixel is calculated.

Description:
BACKGROUND OF THE INVENTION 
   The field of the invention is nuclear magnetic resonance imaging methods and systems. More particularly, the invention relates to the in vivo imaging of metabolites using paramagnetic labels such as hyperpolarized carbon-13. 
   When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B 0 ), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B 1 ) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, Mz, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment Mt. A signal is emitted by the excited spins after the excitation signal B 1  is terminated, this signal may be received and processed to form an image. 
   When utilizing these signals to produce images, magnetic field gradients (G x , G y  and G z ) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received NMR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques. 
   The advent of hyperpolarized (carbon-13) has spurred interest in imaging with this isotope in a variety of in vivo applications such as vascular imaging (MRA) and metabolic flux. One of these is C-13 labeled pyruvate and its metabolites (lactate and alanine), which are of particular interest in oncology applications. The NMR spectrum of these three metabolites is relatively sparse, making them well suited for chemical shift based imaging methods such as those commonly used to separately image water and fat. As shown in  FIG. 2 , these metabolites have a single peak for lactate (Lac), a single peak for alanine (AL) and two peaks for pyruvate (PE and Pyr). In a 3 Tesla polarizing field the chemical frequency shift of alanine is approximately −242 Hz relative to lactate, pyruvate has a main peak at approximately −622 Hz and a pyruvate ester peak lies at approximately −242 Hz relative to lactate. 
   The usual method for imaging these C-13 isotopes uses an echo planar spectroscopic imaging technique that requires the acquisition of large amounts of data. In order to resolve the spectral peaks for AL and PE it is necessary to acquire 64 NMR signal at different echo times. A large amount of data is needed to obtain the needed “spectral resolution” when a Fourier transformation is performed on the data to produce a spectrum. Because of the large amount of data that is acquired, a difficult choice between shorter scan time and higher spatial resolution is usually required. 
   Recently, a new method known as IDEAL was developed for imaging spin species such as fat and water. As described in U.S. Pat. No. 6,856,134 B1 issued on Feb. 15, 2005 and entitled “Magnetic Resonance Imaging With Fat-Water Signal Separation”, the IDEAL method employs pulse sequences to acquire multiple images at different echo times (TE) and an iterative, linear least squares approach to estimate the separate water and fat signal components. The advantage of the IDEAL method is if the frequencies of the particular metabolites being imaged are known, the number of different echo time repetitions can be significantly reduced. This “a priori” information shortens scan time and enables more pulse sequence repetitions to be devoted to increased image resolution. 
   SUMMARY OF THE INVENTION 
   The present invention is a method for producing an MR image of a metabolite where the frequencies of the peak NMR signals produced by the metabolite are known and the relative values of the plurality of NMR peak signals produced by the metabolite are known. Using this a priori information the NMR signal can be modeled with an equation of relatively few unknowns. A corresponding relatively few MR images are acquired of the subject and from this acquired NMR image data and the equation, the signal components corresponding to the metabolite peak signals may be calculated and used to produce a metabolite image. The echo time (TE) is shifted in each of the acquired NMR images and the optimal echo time shift is determined to increase SNR of the measurement. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a block diagram of an MRI system which employs the present invention; 
       FIG. 2  is a graphic representation of the spectra produced by C-13 labeled pyruvate and its metabolites; 
       FIG. 3  is a graphic representation of a preferred pulse sequence used to direct the operation of the MRI system of  FIG. 1 ; 
       FIG. 4  is a graphic representation of the NSA plot for the metabolites of  FIG. 2 ; 
       FIG. 5  is a flow chart illustrating the steps used to practice the preferred embodiment of the invention; and 
       FIG. 6  is a graphic representation of the NSA plot of the metabolites of  FIG. 2  in a four echo acquisition. 
   

   GENERAL DESCRIPTION OF THE INVENTION 
   The present invention enables the spectrum of a metabolite such as C-13 labeled pyruvate and its metabolites lactate and alanine to be efficiently produced when a priori information is known about the metabolites. More specifically, when the frequency of each peak in the metabolite NMR signal is known, this information can be used to substantially reduce the amount of NMR data that needs to be acquired to produce an image of the metabolite. In addition, where a single metabolite produces more than one signal peak, available a priori knowledge about the relative areas of the multiple signal peaks may also be used to substantially reduce the amount of NMR data that needs to be acquired. 
   As shown in  FIG. 2 , the frequencies of the C-13 labeled pyruvate metabolites are known, as is the relative areas of the two pyruvate peaks PE and Pyr. The NMR signal from a voxel containing these three species measured at an echo time t n  is then expressed as follows:
 
 s ( t   n )=( P   A   e   i2πf     A     t     n     +P   L   e   i2πf     L     t     n     +P   P ( r   P1   e   i2πf     P1     t     n     +r   P2   e   i2πf     P2     t     n   )) e   i2πψt     n    
 
where: P A , P L  and P P  are the total signal contributions from alanine, lactate and pyruvate respectively; f A , f L , f P1  and f P2  are the resonant frequencies of alanine, lactate, the main pyruvate peak and pyruvate ester peak; and r P1  and r P2  are the relative fractions of total signal from the two pyruvate peaks (r P1 +r P2 =1.0).
 
   The outer phase term in equation (1) results from the local polarizing magnetic field inhomogeneity (ψ) and this must be removed from the signals S(t n ) before they can be used to compute the metabolite levels. The field inhomogeneity term ψ can be estimated from the acquired signals S(t n ) using an iterative method as described by Reeder et al, MRM, 51(1):123–30, 2004. With this approach at least four signals S(t n ) must be acquired in order to solve for the four unknowns (P A , P L , P P , ψ). Or the inhomogeneity (ψ) can be calculated from a proton density ( 1 H) calibration image that is separately acquired and used to produce a B 0  field inhomogeneity map. In this embodiment only three signals S(t n ) need be acquired since ψ is determined by the separate proton density image acquisition. This map indicates the field inhomogeneity ψ at each image pixel in terms of a shift in the Larmor frequency from the nominal Larmor frequency. The phase created by the field inhomogeneity is demodulated from the acquired NMR signals S(t n ) by multiplying the signal S(t n ) by a phase term e −i2πψt     n    to remove the effects of B 0  field inhomogeneities. 
   With the phase created by the field inhomogeneity removed, equation (1) can be rewritten as follows:
 
S=Aρ  (2)
 
where:
 
                 S   =       ⁢       [       S   ⁡     (     t   TE1     )       ,   S     ]     ⁢     (     t   TE2     )     ⁢           ⁢   …   ⁢           ⁢     S   ⁡     (     t   n     )                     ρ   =       ⁢     [       ρ   A     ,     ρ   L     ,     ρ   P       ]                 A   =       ⁢     [           ⁢           C   1   A           C   1   L           C   1   P               C   2   A           C   2   L           C   2   P             ⋮       ⋮       ⋮             C   n   A           C   n   L           C   n   P           ⁢           ]                 
with
 C n   A   =e   i2πf     A     t     n      C n   L   =e   i2πf     L     t     n        C   n   P =( r   P1   e   i2πf     P1     t     n     +r   P2   e   i2πf     P2     t     n      
If sufficient images are acquired at different echo times TE, all of the terms in the coefficient matrix A are known and estimates of the three metabolites ({circumflex over (P)}) may then be calculated from the pseudo-inverse of equation (2):
   {circumflex over (P)} =( A   H   A ) −1   A   H   S   (3) 
where “ H ” denotes the Hermitian transpose. In the case of C-13 labeled pyruvate, three images are required at a minimum. Obviously, this is a substantial reduction in scan time over prior methods which require 64 images to provide the needed spectral resolution.
 
   Different echo times are needed in the n=3 images and the changes, or shifts in echo time TE can be chosen to maximize the SNR performance of the the effective number of signal averages (NSA). NSA is easily calculated for each species as the inverse of each diagonal term in the covariance matrix:
 
 NSA= 1/(( A   H   A ) −1 ) m,m   (4)
 
where:
         m=1 for alanine,   m=2 for lactate, and   m=3 for pyruvate.       

   The NSA values can be calculated for different echo shifts in order to maximize the NSA for some or all the metabolites, determining the optimum echo spacing that will maximize noise performance. For example,  FIG. 4  shows the NSA performance for three equally spaced echoes for the case where the field map (ψ) is known or measured using an external calibration. From this plot, it can be determined that an echo spacing of approximately 1.0 ms will provide excellent NSA for all three metabolites. This is one possible echo combination that will provide good noise performance for the decomposition of the three species, however other combinations of echoes, including unequally spaced echoes can be used for this form of optimization. 
   More than three echoes can also be used to decompose the three species. Not all pulse sequences are sufficiently flexible in their timing to achieve the optimal echo spacing, for example, 1.0 ms. For this reason it may be advantageous to acquire more than 3 echoes, in order to match the capabilities of the pulse sequence with an optimal echo combination. For example,  FIG. 6  plots the NSA for the same decomposition using 4 echoes. An optimal spacing occurs at spacings of 1.4 ms or 2.1 ms. Thus, if a pulse sequence is unable to achieve an echo spacing of 1.0 ms for performing the preferred 3 echo decomposition, it might be advantageous to perform a four echo acquisition using an echo spacing 1.4 ms or 2.1 ms. 
   DESCRIPTION OF THE PREFERRED EMBODIMENT 
   Referring particularly to  FIG. 1 , the preferred embodiment of the invention is employed in an MRI system. The MRI system includes a workstation  10  having a display  12  and a keyboard  14 . The workstation  10  includes a processor  16  which is a commercially available programmable machine running a commercially available operating system. The workstation  10  provides the operator interface which enables scan prescriptions to be entered into the MRI system. 
   The workstation  10  is coupled to four servers: a pulse sequence server  18 ; a data acquisition server  20 ; a data processing server  22 , and a data store server  23 . In the preferred embodiment the data store server  23  is performed by the workstation processor  16  and associated disc drive interface circuitry. The remaining three servers  18 ,  20  and  22  are performed by separate processors mounted in a single enclosure and interconnected using a 64-bit backplane bus. The pulse sequence server  18  employs a commercially available microprocessor and a commercially available quad communication controller. The data acquisition server  20  and data processing server  22  both employ the same commercially available microprocessor and the data processing server  22  further includes one or more array processors based on commercially available parallel vector processors. 
   The workstation  10  and each processor for the servers  18 ,  20  and  22  are connected to a serial communications network. This serial network conveys data that is downloaded to the servers  18 ,  20  and  22  from the workstation  10  and it conveys tag data that is communicated between the servers and between the workstation and the servers. In addition, a high speed data link is provided between the data processing server  22  and the workstation  10  in order to convey image data to the data store server  23 . 
   The pulse sequence server  18  functions in response to program elements downloaded from the workstation  10  to operate a gradient system  24  and an RF system  26 . Gradient waveforms necessary to perform the prescribed scan are produced and applied to the gradient system  24  which excites gradient coils in an assembly  28  to produce the magnetic field gradients G x , G y  and G z  used for position encoding NMR signals. The gradient coil assembly  28  forms part of a magnet assembly  30  which includes a polarizing magnet  32  and a whole-body RF coil  34 . In the preferred embodiment a 3.0 Tesla scanner sold by General Electric under the trademark “SIGNA” is employed. 
   RF excitation waveforms are applied to the RF coil  34  by the RF system  26  to perform the prescribed magnetic resonance pulse sequence. Responsive NMR signals detected by the RF coil  34  are received by the RF system  26 , amplified, demodulated, filtered and digitized under direction of commands produced by the pulse sequence server  18 . The RF system  26  includes an RF transmitter for producing a wide variety of RF pulses used in MR pulse sequences. The RF transmitter is responsive to the scan prescription and direction from the pulse sequence server  18  to produce RF pulses of the desired frequency, phase and pulse amplitude waveform. The generated RF pulses may be applied to the whole body RF coil  34  or to one or more local coils or coil arrays. 
   The RF system  26  also includes one or more RF receiver channels. Each RF receiver channel includes an RF amplifier that amplifies the NMR signal received by the coil to which it is connected and a quadrature detector which detects and digitizes the I and Q quadrature components of the received NMR signal. The magnitude of the received NMR signal may thus be determined at any sampled point by the square root of the sum of the squares of the I and Q components:
 
 M=√{square root over (I 2 +Q 2 )},  
 
and the phase of the received NMR signal may also be determined:
 
φ= −1   Q/I.  
 
In the preferred embodiment a dual-tuned, proton-carbon transmit and receive local coil is employed such as that described in U.S. Pat. No. 4,799,016 entitled “Dual Frequency NMR Surface Coil.”
 
   The pulse sequence server  18  also optionally receives patient data from a physiological acquisition controller  36 . The controller  36  receives signals from a number of different sensors connected to the patient, such as ECG signals from electrodes or respiratory signals from a bellows. Such signals are typically used by the pulse sequence server  18  to synchronize, or “gate”, the performance of the scan with the subject&#39;s respiration or heart beat. 
   The pulse sequence server  18  also connects to a scan room interface circuit  38  which receives signals from various sensors associated with the condition of the patient and the magnet system. It is also through the scan room interface circuit  38  that a patient positioning system  40  receives commands to move the patient to desired positions during the scan. 
   It should be apparent that the pulse sequence server  18  performs real-time control of MRI system elements during a scan. As a result, it is necessary that its hardware elements be operated with program instructions that are executed in a timely manner by run-time programs. The description components for a scan prescription are downloaded from the workstation  10  in the form of objects. The pulse sequence server  18  contains programs which receive these objects and converts them to objects that are employed by the run-time programs. 
   The digitized NMR signal samples produced by the RF system  26  are received by the data acquisition server  20 . The data acquisition server  20  operates in response to description components downloaded from the workstation  10  to receive the real-time NMR data and provide buffer storage such that no data is lost by data overrun. In some scans the data acquisition server  20  does little more than pass the acquired NMR data to the data processor server  22 . However, in scans which require information derived from acquired NMR data to control the further performance of the scan, the data acquisition server  20  is programmed to produce such information and convey it to the pulse sequence server  18 . For example, during prescans NMR data is acquired and used to calibrate the pulse sequence performed by the pulse sequence server  18 . Also, navigator signals may be acquired during a scan and used to adjust RF or gradient system operating parameters or to control the view order in which k-space is sampled. And, the data acquisition server  20  may be employed to process NMR signals used to detect the arrival of contrast agent in an MRA scan. In all these examples the data acquisition server  20  acquires NMR data and processes it in real-time to produce information which is used to control the scan. 
   The data processing server  22  receives NMR data from the data acquisition server  20  and processes it in accordance with description components downloaded from the workstation  10 . Such processing include Fourier transformation of raw k-space NMR data to produce two or three-dimensional images; the application of filters to a reconstructed image and the reconstruction of the metabolic images according to the present invention. 
   Images reconstructed by the data processing server  22  are conveyed back to the workstation  10  where they are stored. Real-time images are stored in a data base memory cache (not shown) from which they may be output to operator display  12  or a display  42  which is located near the magnet assembly  30  for use by attending physicians. Batch mode images or selected real time images are stored in a host database on disc storage  44 . When such images have been reconstructed and transferred to storage, the data processing server  22  notifies the data store server  23  on the workstation  10 . The workstation  10  may be used by an operator to archive the images, produce films, or send the images via a network to other facilities. 
   A number of different pulse sequences can be used to direct the MRI system to acquire the data needed to practice the present invention. In the preferred embodiment a pulse sequence as shown in  FIG. 3  is employed which uses the steady state free precision (SSFP) principle. It includes a selective rf excitation pulse  50  that is repeated at the start of each TR period as well as a slice select gradient pulse  52  that is produced concurrently with the rf pulse  50  to produce transverse magnetization in a prescribed slice. After excitation of the spins in the slice a phase encoding gradient pulse  54  is applied to position encode the NMR signal  56  along one direction in the slice. A readout gradient pulse  58  is also applied after a dephasing gradient lobe  60  to position encode the NMR signal  56  along a second, orthogonal direction in the slice. The NMR signal  56  is sampled during a data acquisition window  62 . To maintain the steady state condition, the integrals of the three gradients each sum to zero. To accomplish this rephrasing lobes  64  are added to the slice select gradient waveform, a rephrasing lobe  66  is added to the readout gradient waveform and a rewinder gradient lobe  68  is added to the phase encoding gradient waveform. As is well known in the art, the pulse sequence is repeated and the amplitude of the phase encoding gradient  54  and its equal, but opposite rewinder  68  are stepped through a set of values to sample 2D k-space in a prescribed manner. As will be explained in more detail below, each slice is acquired three or more times and the echo time TE increment is set to 1.0 ms during successive acquisitions. 
   Referring particularly to  FIG. 5 , the first step in performing a C-13 metabolite scan is to prepare the subject as indicated at process block  100 . This includes injection of nonhyperpolarized or hyperpolarized C-13 labeled pyruvate from a suitable source such as a polarizer device. 
   A scan is then conducted with the above MRI system using the above described pulse sequence to acquire spectroscopic image data as indicated at process block  102 . Three images at three different echo times TE are acquired at each prescribed slice location. This provides sufficient information when combined with a prior information concerning the metabolite signal to produce images of the metabolites alanine, lactate and pyruvate. 
   As indicated at process block  104  the next step is to reconstruct the three images at each slice location. This is done in the usual manner by performing a two-dimensional, complex Fourier transformation of the acquired k-space data. As a result, three NMR signals S(t TE1 ), S(t TE2 ) and S(t TE3 ) are produced for each pixel location in each slice. 
   A field map (ψ) is produced next as indicated at process block  106 . As indicated above, this can be done by either using an iterative method described by S. B. Reeder et al in “Multicoil Dixon Chemical Species Separation With An Iterative Least-Squares Estimation Method”, MRM, 51:35–45 (2004), or a separate scan can be performed to acquire a proton calibration image from which the phase error ψ is determined at each image pixel as discussed above. The phase shifts caused by inhomogeneities in the scanner polarizing magnetic field are then demodulated from the images as described above and indicated at process block  108 . 
   As indicated at process block  110 , the metabolite component of the signals at each slice image pixel is then calculated using the corrected image signals S(t TE1 ), S(t TE2 ) and S(t TE3 ) and the above equation (3). The values of the metabolite signals ρ A , ρ L  and ρ P  are thus calculated at each slice image pixel. These can be displayed as separate metabolite images as indicated at process block  112 , or the three separate metabolite images can be combined into a single image with different color coding for each metabolite. It is also possible to acquire during the scan a proton image and reconstruct a high resolution anatomical image of each slice. The metabolite image or images may be registered and displayed in color with the anatomical image forming a black and white background. 
   It should be apparent to those skilled in the art that many variations are possible from the above described preferred embodiment. For example, many other pulse sequences can be used to acquire the NMR data and different image reconstruction methods can be used. For example, a pulse sequence that samples k-space along a radial path can be used and the images reconstructed using a backprojection technique. Also, other metabolites may be imaged using the present invention where sufficient a priori information is known about the frequency of their NMR signal peaks and the relative values of their multiple peaks. 
   The decomposition described in Equations 1–3 is preferably performed in image space. So long as the field map (ψ) can be ignored or has been demodulated from the source data, the signal, as described in Equation 1 is a linear system, which will also hold after Fourier transformation into k-space. This permits separation of the k-space signals of the chemical species into separate data matrices. After separation of the k-space data, the Fourier transform is performed to yield images of each metabolite. In general, however, it is more convenient to perform calculations in image space if the field map (which makes Equation 1 a non-linear equation) is non-zero, creating position dependent phase shifts.