Methods and apparatus for magnetic resonance imaging

A system for generating magnetic resonance images includes an MRI scanner for obtaining data from a pre-scan and data from a selected scan. A processor determines whether the data from the selected scan includes errors based on the data from the pre-scan, and requests the MRI scanner to reacquire the data from the selected scan if data is found to include errors, or converts the data from the selected scan to an image if no error is found. A display device displays the image converted by the processor.

FIELD OF THE INVENTION

A field of the invention is magnetic resonance (MR) imaging. The invention particularly concerns processing of data from an MRI scanner.

BACKGROUND OF THE INVENTION

A known magnetic resonance imaging (MRI) scanner10is shown inFIG. 1. A patient12is slid axially into a bore14of a superconducting magnet16, and the main magnetic field is set up along the axis of the bore, the Z-direction. Magnetic field gradients are set up, for example, in the Z-direction, to confine the excitation of magnetic resonant (MR) active nuclei (typically hydrogen protons in water and fat tissue) to a particular slice in the Z-direction, in the horizontal X and the vertical Y-directions (as shown inFIG. 1), to encode the resonant MR nuclei in the plane of the slice. A radio frequency (RF) transmit coil (not shown) applies an excitation pulse to excite the protons to resonance, and an RF receive coil arrangement comprising an array of receive coils18,20picks up relaxation signals emitted by the disturbed protons.

To encode/decode received signals in the Y-direction, the signals are detected in the presence of a magnetic field gradient, termed a frequency encode or read-out (R.O.) gradient, to enable different positions of relaxing nuclei to correspond to different precession frequencies of those nuclei about the direction of the main magnetic field due to the influence of the gradient. The data is digitized, and so for each RF excitation pulse, a series of digital data points are collected, and these are mapped into a spatial frequency domain known as k-space (FIG. 2). Each RF pulse permits at least one column of digital data points to be collected. The set of data points acquired during one read-out event (for example, one column ofFIG. 2) is commonly referred to as a “line” of data.

To encode/decode the received signals in the X-direction, after each RF pulse has been transmitted and before data is collected with the read-out gradient applied, a magnetic field gradient in the X-direction is turned on and off. This is done for a series of magnitudes of magnetic field gradients in the X-direction, one RF pulse typically corresponding to a different magnitude of gradient in the X-direction. On the k-space matrix shown inFIG. 2, the columns of data points correspond to data collected at different magnitudes of phase-encode (PE) gradients.

Generally, the field of view imaged by the magnetic resonance imaging scanner10depends on the spacing of the data points in the phase-encode and read-out directions, and the resolution of the image depends on how far the points extend in each direction, i.e., how large the maximum phase-encode gradient is, and on the magnitude of the read-out gradient combined with the duration of data collection. Conventionally, the data collected by the RF receive coils18,20is subject to a two-dimensional fast Fourier transform to produce a pixelated spatial image. A slice image A is shown inFIG. 3, which corresponds to area A of the patient10shown inFIG. 1.FIG. 3implies that the spacing of data points in the phase-encode gradient direction is sufficient to image the whole of the circle shown inFIG. 1.

Between each RF pulse, there is a certain minimum pulse repetition time, and the collection of a complete set of phase encode data implied byFIG. 2may therefore take an undesirably long time. Parallel imaging is an MR imaging technique that uses multiple detectors (phased array coils) to partially replace phase encoding. Each coil measures a set of k-space data points that differ from each other because of the different spatial location and sensitivity of the coils, so the total number of unique measurements is a multiple of the number of coils. For example, if N data points are needed to make an image, these can be obtained from N measurements using one coil or from (N/R) measurements using R coils. Thus parallel imaging is quicker by a factor of up to R. This reduces acquisition times by decreasing the number of phase-encoded lines of k-space that must be acquired. Usually the phase encode data points sampled in parallel imaging are more widely spaced so they cover the same area but with reduced density. Practical implementation of parallel imaging includes SENSE (sensitive encoding) which operates in the image domain, and SMASH (simultaneous acquisition of spatial harmonics) that operates in the k-space matrix.

Navigation refers to an MR imaging technique that is applied during the scan to determine if patient motion has occurred, typically respiratory motion. Navigation uses multiple measurements of a reference part of the anatomy to detect positional changes. If such changes are detected, the affected data points resulting from the motion are corrected or re-acquired. The parallel imaging technique SMASH has been proposed as a way of doing navigation by using previously acquired data to predict the data that have yet to be acquired. Predictions can be adversely affected by systematic errors arising from SMASH data processing and also random errors from low signal to noise ratio (SNR), which reduce the accuracy of the navigation.

Partial Fourier is a technique that reduces the amount of data that is acquired to reduce the MR scan time. Partial Fourier does this by applying certain processing steps (phase correction) that allow one to make the assumption that one half of the k-space data is almost identical to the other half. Therefore, only a little over half the data is needed to make an image.

SUMMARY OF THE INVENTION

A system for generating magnetic resonance images includes an MRI scanner for obtaining data from a pre-scan and data from a selected scan. A processor determines whether the data from the selected scan includes errors based on its consistency with the data from the pre-scan, and requests the MRI scanner to reacquire the data from the selected scan if data is found to include errors, or converts the data from the selected scan to an image if no error is found. A display device displays the image converted by the processor.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The invention is directed to methods and apparatus for generating an image of a portion of a patient scanned by an MRI scanner. In one embodiment of the invention, a processor determines in real-time whether data obtained from a scan contains errors, for example, due to patient motion. If unacceptable level of errors are detected, data is rejected and reacquired from the MRI scanner without converting the data to an image, thereby ensuring that all the accepted data meet a minimum criterion in regard to the acceptable level of error. In another embodiment of the invention, data obtained from the MRI scanner is used to create an image, which is then reconstructed a number of times to suppress poor quality data points which may arise due to patient motion or hardware imperfections. In yet another embodiment of the invention, data from the MRI scanner is obtained in a pattern which would allow creation of an image combining both the partial Fourier imaging method and the parallel imaging method, thereby reducing scan time, and also artifacts and noise in the image.

Turning now toFIG. 4, one embodiment of the invention for performing magnetic resonance (MR) imaging involves a magnetic resonance imaging (MRI) system22including an MRI scanner24, a processor26and a display28. The MRI scanner24collects data representing a slice of an area of a patient. The processor26receives the data obtained by the MRI scanner24and converts the data to an image, which is shown on the display28.

Referring toFIG. 5, one embodiment of the present MRI system22for processing data from the MRI scanner24includes performing a pre-scan to get coil sensitivity maps (block30). Pre-scanning generally includes running an additional scan (pre-scan) of the same object as the selected scan prior to the selected scan when the MRI scanner24receives an instruction to start. Some of the scan parameters must be the same for both the pre-scan and the selected scan (i.e., the field of view and slice thickness) but other parameters need not be. Thus, the duration of the pre-scan can made be much shorter (for example, less than 1 second).

The data from the pre-scan is passed from the MRI scanner24to the processor26. The selected scan is then started by the MRI scanner24(block32) and the phase encode data obtained from this scan is passed to the processor26as they are received. Using the data from the pre-scan and the selected scan, the processor26determines whether the data obtained from the selected scan contains errors, due to patient motion, for example (block34). If so, the data from the selected scan is rejected (block36) and an instruction is sent from the processor26to the MRI scanner24to reacquire the phase encode data of the selected scan. Otherwise, the phase encode data is accepted (block38), and a determination is made as to whether a full data set has been acquired (block40). If full data set has not been acquired, the next phase encode data of the selected scan is acquired (block32), and the same error checks are performed on next phase encode data (block34). When a full data set has been acquired, the processor26converts the data set to an image (block42) and sends the image to the display28(block44).

One embodiment of an algorithm that determines whether the acquired data contains errors (block32) has been named “Parallel Imaging Navigators” (PINs). The PINs algorithm makes use of the SENSE parallel imaging reconstruction, which is concisely expressed as a linear equation,
A.x=b  (1)
where A is a sensitivity matrix determined from the pre-scan, x is a vector of the desired pixel values in the image, and b is a vector containing the raw k-space data from the selected scan.

After a phase encode data has been acquired, the data set consists of all previous phase encode data plus the newly acquired one, which is possibly corrupt if the patient moved. The above equation (1) is solved both with and without the newly acquired data, and the two solutions are compared. Specifically, one solution is obtained from equation (1) using all of the acquired data from the selected scan, which comprises the previous phase encode data plus the newly acquired phase encode data, and a second solution is obtained from equation (1) using the previous phase encode data only and not the newly acquired phase encode data. In this application the equation is often numerically unstable so numerical regularization is necessary, for example, using standard techniques such as truncated singular value decomposition.

The way the comparison is made is by making a Fourier transform of the two solutions (x) so that they are in k-space, and then taking the difference. In this embodiment, the area of k-space that is supported by the previously acquired data is of interest. If the newly acquired data does not contain errors, the difference will be small, whereas if it does contain errors the difference will be large. In one embodiment, a “cost” function is used to specify the magnitude of the error, namely the sum of the absolute difference between the solutions divided by the sum of the absolute values of the solution obtained without the new data. This cost function only produces positive values, and if its value is greater than approximately 1 then the new data is deemed to contain unacceptable errors. If the value of the cost function is approximately between 0 and 1 then the data is deemed to be within acceptable error. The decision as to whether the new data contains errors is based on the size of the cost function. The threshold value (equal to approximately 1, for example) may be decreased or increased to vary how stringent the acceptable error level should be.

In accordance with another embodiment of the invention, MR data sets received from the MRI scanner24(best shown inFIG. 4) is reconstructed using a robust method to resist corrupted data. The term “robust” as used in this patent refers to a mathematical term that relates to the detection of “outliers”, i.e., corrupt data points, in a data set and reducing their impact on image reconstruction.

Turning now toFIG. 6, a method for performing robust reconstruction in accordance with one embodiment of the invention includes performing a pre-scan in the MRI scanner24and passing the data from the pre-scan to the processor26(block46). Then a selected scan of the subject is started by the MRI scanner24, and the resulting data passed to the processor26(block48). Once both scans are completed, the processor26creates an image using a partially parallel image reconstruction such as the SENSE reconstruction technique (block50). The processor26then uses an algorithm (described below) to repeatedly reconstruct the image in such a way as to suppress poor quality data points (block52). Poor quality data points may arise due to, for example, patient motion or hardware imperfections. The final image is then passed to the display28(block54).

One embodiment of the algorithm for repeatedly reconstructing the image (block52) includes solving the equation,
W.A.x=W.b  (2)
where W is a diagonal weighting matrix, A is a sensitivity matrix determined from the pre-scan, x is the desired pixel values in the image, and b is the raw k-space data from the normal scan. Equation (2) is a linear equation describing a parallel imaging image reconstruction based on SENSE.

Turning now toFIG. 7, the processor26arranges the acquired data into a form suitable for the SENSE reconstruction using equation (2). In block56, the processor26solves for x in equation (2) using values for A (obtained from the pre-san) and b (k-space data from the selected scan), and setting W initially to the identity matrix. The value obtained for x is then used to define r=A.x−b (block58). W is then updated as a function of r, which is denoted f(r) (block60). The process returns to block56now using the new W obtained in block60. The process in blocks56–60are repeated approximately 10 times, for example, after which the resulting image (x) is passed to the display28.

In one embodiment, Huber function (f(r)=min {1, c/¦r¦}), is employed in obtaining the weighting factors W. It should understood, however, that many other weighting factors (also known as M-estimators) may also be used, such as, for example, Cauchy (f(r)=1/(1+(r/c)2)); Fair (f(r)=1/(1+¦r/c¦)); Welsch f(r)=exp(−(r/c)2), where c is a constant scaling factor equal to some multiple of the median value of |r|. The value of c determines how strongly the outliers are suppressed. For example, c=3. median(|r|) is a “medium” value, whereas c=1. median(|r|) indicates strong suppression, and c=5. median(|r|) indicates not very strong suppression.

In accordance with another embodiment of the present invention, hereinafter referred as a partial Fourier partially parallel (PFPP) imaging method, is used to reduce scan times in the MRI scanner24. Generally, PFPP imaging method combines the speed advantages of the partial Fourier and the partially parallel imaging techniques. The partial Fourier technique of acquiring half the data is used with the parallel imaging method of reducing the number of measurements, resulting in shortened scan times and less noise in images.

Turning toFIGS. 8–10, various data sampling patterns are illustrated.FIG. 8is a data sampling pattern (e.g., 256 phase encode lines of data) obtained by an MRI scanner without using any time reducing methods. This method typically results in high quality image, but suffers from lengthy scan time.FIG. 9shows a sampling pattern obtained using a partial Fourier method, which requires less lines of data (e.g., 136 lines), and therefore, reduced scan time. This method, however, is prone to more artefacts. Parallel Imaging method, as shown inFIG. 10, requires even less lines of data (e.g., 100 lines) and less time than the partial Fourier method, but is prone to noise. In the present context, “artifacts” are considered to be aberrations in the image, such as bright spots or smearing effects, that do not correctly represent the spatial properties of the object. “Noise” is considered a random speckling effect on the image that tends to obscure fine detail, and is the visual equivalent of static on radio signals.

FIG. 11shows a k-space sampling patterns obtained in accordance with the PFPP imaging method of the present invention. The PFPP imaging method requires less data (e.g., 86 lines) than either the partial Fourier method or the parallel imaging method, and accordingly, less scan time than these two methods separately. As shown in theFIG. 11, the central region56of the data (which typically refers to the data within an area approximately 16 to 32 points of the middle of the k-space matrix) is fully sampled (i.e., as inFIG. 8, without any time reducing methods) to provide phase information to do partial Fourier and coil sensitivity information to do the parallel imaging reconstruction.

As described above, coil sensitivity information is what is usually measured in a pre-scan. It is necessary to obtain this information when using the partial Fourier or parallel imaging techniques. In this embodiment, instead of using a pre-scan, another known technique is to incorporate the necessary measurements into the second scan, which means just a single scan is made but the central region56is acquired at full density. This is known as “auto calibration” or homodyne detection.

Referring back toFIG. 4, in the PFPP imaging method of the invention, data in the pattern described above with respect toFIG. 11is acquired by the MRI scanner24by programming the scanner to obtain the data in that specified pattern. The MRI scanner24is programmed using software tools provided by the manufacturer, and the scanner is typically instructed to acquire a central region corresponding to approximately ⅛ththe size of the k-space matrix plus a number of measurements spread over the outer areas of the k-space matrix. For example, if the k-space matrix were of dimensions 256×256 then the acquired data set might consist of 32 central lines plus 64 lines covering the outer areas of the k-space matrix. Both sides of the k-space matrix may be covered or one side only. The number of lines and their pattern of distribution within the k-space matrix are varied to alter the overall time taken for the scan and the image quality (i.e. noise level, artifact level). Specific choices depend on the scanner used, the number of coil receivers and the requirements of the scan. For example, with a 256×256 k-space matrix a fast scan producing a moderate quality image may comprise 32 central lines and 32 outer lines covering one side of k-space; whereas a higher quality scan may comprise 32 central lines and 128 outer lines covering both sides of k-space. In the latter case the outer lines are arranged so that they are not in “conjugate symmetric” pairs, which means if the k-space matrix is folded in half then the outer lines will not over-lap each other. Following the data acquisition, the data is passed on to the processor26, where it is processed using an algorithm (discussed below) to generate an image. The obtained image is passed to the display28.

The algorithm for generating image in the processor26in the PFPP imaging technique includes performing a parallel imaging reconstruction, i.e., solving the equation,
A.x=b  (3)
constrained so that the solution (x) also obeys the requirements of partial Fourier. This requires that the imaginary part of x be zero. This is brought about by separating equation (3) into real and imaginary parts and regularizing the imaginary part, i.e.,

[Re⁢⁢{b}Im⁢⁢{b}0]=[Re⁢⁢{A}Im⁢⁢{-A}Im⁢⁢{A}Re⁢⁢{A}0λ⁢⁢I]⁢[Re⁢⁢{x}Im⁢⁢{x}](4)
where, A is a sensitivity matrix determined from the fully sampled central region56of data (best shown inFIG. 11), x is the desired pixel values in the final image, b is the raw k-space data from the scan, I is the identity matrix and λ is a scalar to weaken/strengthen the constraint. In one embodiment, the known. “sum-of-squares” coil modulation is used when making the sensitivity matrix.

One example of a computer algorithm that implements this expression is as follows:

In accordance with the PFPP imaging method of the invention, less data is required than either partial Fourier or partially parallel imaging to generate image from the MRI scanner24. By varying the parameter λ, the PFPP imaging method can be adjusted to offer the advantages of fewer artefacts than partial Fourier and less noise than partially parallel imaging.

The PFPP imaging method of the invention may be combined with the robust reconstruction method of the invention described above for outlier suppression by substituting the following equation (5) in place of equation (2) and using equation (5) in the block56ofFIG. 7:

[Wr000Wi000Wλ]⁢[Re⁢⁢{b}Im⁢⁢{b}0]=[Wr000Wi000Wλ]⁢[Re⁢⁢{A}Im⁢⁢{-A}Im⁢⁢{A}Re⁢⁢{A}0λ⁢⁢I]⁢[Re⁢⁢{x}Im⁢⁢{x}](5)
where Wr, Wiand Wλare diagonal weighting matrices. Different weighting functions described above can be used for each weighting matrix. In one embodiment Wλis fixed equal to the identity matrix. The result of this substitution is an enhancement of the error suppression compared with the images produced by equation (2).