CALCULATION OF A B0 IMAGE MULTIPLE DIFFUSION WEIGHTED MR IMAGES

Abstract

The invention provides for a medical imaging system (100, 300). The execution of the machine executable instructions (110) causes a processor (102) to: receive (200) multiple diffusion weighted images (112) of a subject (318), wherein the multiple diffusion weighted images each have an assigned b-value, wherein the multiple diffusion weighted images each have an assigned diffusion weighting direction, wherein for a region of interest (309) there is at least one corresponding voxel (506) in each of the multiple diffusion weighted images; construct (202) a set of equations (114) for each of the at least one corresponding voxel, wherein the set of equations is constructed from an apparent diffusion equation for the assigned diffusion weighting direction of each of the multiple diffusion weighted images; solve (204) the set of equations for each voxel for the b.sub.0 value as an optimization; and construct (206) a image using the b.sub.0 value for each voxel.

Claims

1. A medical imaging system comprising: a memory for storing machine executable instructions; a processor for controlling the medical imaging system, wherein execution of the machine executable instructions causes the processor to: receive multiple diffusion weighted images of a subject, wherein the multiple diffusion weighted images each have an assigned b-value representing the diffusion weighting strength, wherein the multiple diffusion weighted images each have an assigned diffusion weighting direction, wherein for a region of interest there is at least one corresponding voxel in each of the multiple diffusion weighted images; construct a set of equations for each of the at least one corresponding voxel, wherein the set of equations is constructed from an apparent diffusion equation for the assigned diffusion weighting direction of each of the multiple diffusion weighted images; solve the set of equations for each voxel for a b.sub.0-value representing zero diffusion weighting as an optimization; and construct b.sub.0 image using the b.sub.0 value for each voxel, where the b.sub.0-value corresponds to image intensity at no diffusion weighting.

2. The medical imaging system of claim 1, wherein execution of the machine executable instructions further causes the processor to calculate an image intensity correction of at least one of the multiple diffusion weighted images using the b.sub.0 image to correct for gradient non-linearity.

3. The medical imaging system of claim 2, wherein the image intensity correction is calculated in each assigned diffusion weighting direction.

4. The medical imaging system of claim 1, wherein the medical imaging system further comprises a magnetic resonance imaging system, wherein the memory further contains pulse sequence commands configured to control the magnetic resonance imaging system to acquire magnetic resonance imaging data according to a diffusion weighted magnetic resonance imaging protocol, wherein execution of the machine executable instructions further cause the processor to: control the magnetic resonance imaging system with the pulse sequence commands to acquire the magnetic resonance imaging data; and reconstruct the multiple diffusion weighted images using the magnetic resonance imaging data.

5. The medical imaging system of claim 1, wherein execution of the machine executable instructions further causes the processor to perform a motion correction between the multiple diffusion weighted images before constructing the set of equations.

6. The medical imaging system of claim 1, wherein the multiple diffusion weighted images are EPI multiple diffusion weighted images, wherein execution of the machine executable instructions further causes the processor to perform an EPI distortion correction on the multiple diffusion weighted images before constructing the set of equations.

7. The medical imaging system of claim 1, wherein each of the set of equations is constructed by setting a logarithm of the measured intensity of a voxel equal to b.sub.0 plus b-value terms times apparent diffusion coefficient terms for each diffusion direction.

8. The medical imaging system of claim 1, wherein the optimization is solved as an exponential fit over b-values in each of the set of equations.

9. The medical imaging system of claim 1, wherein the b-value for one of the multiple diffusion weighted images is 0.

10. The medical imaging system of claim 1, wherein execution of the machine executable instructions further causes the processor to calculate apparent diffusion coefficients for each voxel during solution of the set of equations for each voxel for the b.sub.0 value.

11. The medical imaging system of claim 10, wherein execution of the machine executable instructions further causes the processor to calculate corrected apparent diffusion coefficients using the b.sub.0 image.

12. A method of medical imaging, wherein the method comprises: receiving multiple diffusion weighted images of a subject, wherein the multiple diffusion weighted images each have an assigned b-value representing the diffusion weighting strength, wherein the multiple diffusion weighted images each have an assigned diffusion weighting direction, wherein for a region of interest there is at least one corresponding voxel in each of the multiple diffusion weighted images; constructing a set of equations for each of the at least one corresponding voxel, wherein the set of equations is constructed from an apparent diffusion equation for the assigned diffusion weighting direction of each of the multiple diffusion weighted images; solving the set of equations for each voxel for a b.sub.0 value representing zero diffusion weighting as an optimization; and constructing a b.sub.0 image using the b.sub.0 value for each voxel, where the b.sub.0 value corresponds to image intensity at no diffusion weighting.

13. The method of claim 12, wherein the method further comprises calculating an image intensity correction of at least one of the multiple diffusion weighted images using the b.sub.0 image to correct for gradient non-linearity.

14. A computer program product comprising machine executable instructions for execution by a processor controlling a medical imaging system, wherein execution of the machine executable instructions causes the processor to: receive multiple diffusion weighted images of a subject, wherein the multiple diffusion weighted images each have an assigned b-value representing the diffusion weighting strength, wherein the multiple diffusion weighted images each have an assigned diffusion weighting direction, wherein for a region of interest there is at least one corresponding voxel in each of the multiple diffusion weighted images; construct a set of equations for each of the at least one corresponding voxel, wherein the set of equations is constructed from an apparent diffusion equation for the assigned diffusion weighting direction of each of the multiple diffusion weighted images; solve the set of equations for each voxel for abo value representing zero diffusion weighting as an optimization; and construct a b.sub.0 image using the b.sub.0 value for each voxel, where the b.sub.0 value corresponds to image intensity at no diffusion weighting.

15. The computer program product of claim 14, wherein the medical imaging system further comprises a magnetic resonance imaging system, wherein execution of the machine executable instructions further causes the processor to: control the magnetic resonance imaging system with pulse sequence commands to acquire magnetic resonance imaging data, wherein the pulse sequence commands configured to control the magnetic resonance imaging system to acquire magnetic resonance imaging data according to a diffusion weighted magnetic resonance imaging protocol; reconstruct the multiple diffusion weighted images using the magnetic resonance imaging data.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In the following preferred embodiments of the invention will be described, by way of example only, and with reference to the drawings in which:

[0053] FIG. 1 illustrates an example of a medical imaging system;

[0054] FIG. 2 shows a flow chart which illustrates a method of operating the medical imaging system of FIG. 1;

[0055] FIG. 3 illustrates a further example of a medical imaging system;

[0056] FIG. 4 shows a flow chart which illustrates a method of operating the medical imaging system of FIG. 3; and

[0057] FIG. 5 shows several grids which represent a collection of multiple diffusion weighted images.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0058] Like numbered elements in these figures are either equivalent elements or perform the same function. Elements which have been discussed previously will not necessarily be discussed in later figures if the function is equivalent.

[0059] FIG. 1 illustrates an example of a medical imaging system 100. In the example in FIG. 1 the medical imaging system is a workstation for image processing. The medical imaging system 100 is shown as comprising a computer 101. The computer 101 comprises a processor 102. The processor 102 is intended to represent one or more processors and may also represent processors distributed to multiple computer systems. The processor 102 is shown as being connected to an optional hardware interface 104. The hardware interface 104 may for example enable the processor 102 to control other components of the medical imaging system 100 and may also be a network interface. The processor 102 is shown as being further connected to a user interface 106.

[0060] The user interface 106 may for example be used for displaying information and/or receiving commands from an operator. The processor 102 is shown as being further connected to a memory 108. The memory 108 may be any combination of memory which is accessible to the processor 102. This may include such things as main memory, cached memory, and also non-volatile memory such as flash RAM, hard drives, or other storage devices. In some examples the memory 108 may be considered to be a non-transitory computer-readable medium.

[0061] The memory 108 is shown as containing machine-executable instructions 110. The machine-executable instructions 110 enable the processor 102 to control the various operation and function of the medical imaging system 100 as well as perform various data and image manipulation tasks.

[0062] The memory 108 is shown as further containing multiple diffusion weighted images 112. They may for example have been received via a network or other storage medium. The memory 108 is further shown as containing a set of equations 114. The set of equations were constructed from an apparent diffusion equation using the multiple diffusion weighted images 112. The memory 108 is further shown as containing a b.sub.0 image 116 that was constructed by solving the set of equations 114 using an optimization. The optimization may for example be programmed into the machine-executable instructions 110.

[0063] The memory 108 is shown as containing an optional apparent diffusion coefficients. When the set of equations 114 are solved they may also be simultaneously solved for the apparent diffusion coefficients. The memory 108 is further shown as containing an intensity corrected multiple diffusion weighted images 120. These are the multiple diffusion weighted images 112 that have been corrected using the b.sub.0 image to correct for gradient non-linearity.

[0064] FIG. 2 shows a flowchart which illustrates a method of operating the medical imaging system 100 of FIG. 1. First in step 200, the multiple diffusion weighted images 112 are received. Each of the multiple diffusion weighted images has an assigned b-value. The multiple diffusion weighted images each have an assigned diffusion weighting direction. For a region of interest there is at least one corresponding voxel in each of the multiple diffusion weighted images. Next in step 202 the set of equations 114 is constructed for each of the at least corresponding voxel.

[0065] The set of equations is constructed from an apparent diffusion equation for the assigned diffusion weighting direction for each of the multiple diffusion weighted images. Then, in step 204, the set of equations 114 are solved for each voxel for the b0 value as an optimization. Then, in step 206, the b.sub.0 image is constructed using the b.sub.0 value for each voxel. In step 208 optionally there is an image intensity correction which is calculated for at least one of the multiple diffusion weighted images 112 using the b.sub.0 image 116 to correct for gradient non-linearity. This results in the intensity corrected multiple diffusion weighted images 120.

[0066] FIG. 3 illustrates a further example of a medical imaging system 300. The medical imaging system 300 in FIG. 3 further comprises a magnetic resonance imaging system 302. The magnetic resonance imaging system 302 comprises a magnet 304. The magnet 304 is a superconducting cylindrical type magnet with a bore 306 through it. The use of different types of magnets is also possible; for instance it is also possible to use both a split cylindrical magnet and a so called open magnet. A split cylindrical magnet is similar to a standard cylindrical magnet, except that the cryostat has been split into two sections to allow access to the iso-plane of the magnet, such magnets may for instance be used in conjunction with charged particle beam therapy.

[0067] An open magnet has two magnet sections, one above the other with a space in-between that is large enough to receive a subject: the arrangement of the two sections area similar to that of a Helmholtz coil. Open magnets are popular, because the subject is less confined. Inside the cryostat of the cylindrical magnet there is a collection of superconducting coils. Within the bore 306 of the cylindrical magnet 104 there is an imaging zone 108 where the magnetic field is strong and uniform enough to perform magnetic resonance imaging. A region of interest 309 is shown within the imaging zone 308. The magnetic resonance data that is acquired typically acquired for the region of interest. A subject 318 is shown as being supported by a subject support 320 such that at least a portion of the subject 318 is within the imaging zone 308 and the region of interest 309.

[0068] Within the bore 306 of the magnet there is also a set of magnetic field gradient coils 310 which is used for acquisition of preliminary magnetic resonance data to spatially encode magnetic spins within the imaging zone 308 of the magnet 304. The magnetic field gradient coils 310 connected to a magnetic field gradient coil power supply 312. The magnetic field gradient coils 310 are intended to be representative. Typically magnetic field gradient coils 310 contain three separate sets of coils for spatially encoding in three orthogonal spatial directions. A magnetic field gradient power supply supplies current to the magnetic field gradient coils. The current supplied to the magnetic field gradient coils 310 is controlled as a function of time and may be ramped or pulsed.

[0069] Adjacent to the imaging zone 308 is a radio-frequency coil 314 for manipulating the orientations of magnetic spins within the imaging zone 308 and for receiving radio transmissions from spins also within the imaging zone 308. The radio frequency antenna may contain multiple coil elements. The radio frequency antenna may also be referred to as a channel or antenna. The radio-frequency coil 314 is connected to a radio frequency transceiver 316. The radio-frequency coil 314 and radio frequency transceiver 316 may be replaced by separate transmit and receive coils and a separate transmitter and receiver. It is understood that the radio-frequency coil 314 and the radio frequency transceiver 316 are representative. The radio-frequency coil 314 is intended to also represent a dedicated transmit antenna and a dedicated receive antenna. Likewise the transceiver 316 may also represent a separate transmitter and receivers. The radio-frequency coil 314 may also have multiple receive/transmit elements and the radio frequency transceiver 316 may have multiple receive/transmit channels. For example if a parallel imaging technique such as SENSE is performed, the radio-frequency could 314 will have multiple coil elements. The transceiver 316 and the gradient controller 312 are shown as being connected to the hardware interface 104 of the computer system 101.

[0070] The memory 108 is further shown as containing pulse sequence commands 320. The pulse sequence commands 320 are commands or data which can be converted into such commands that control the magnetic resonance imaging system 302 to acquire magnetic resonance imaging data according to a diffusion weighted imaging magnetic resonance imaging protocol. The memory 108 is shown as further containing magnetic resonance imaging data 322 that was acquired by controlling the magnetic resonance imaging system 302 with the pulse sequence commands 320.

[0071] FIG. 4 shows a flowchart which illustrates a method of operating the medical imaging system 300 of FIG. 3. First in step 400 the magnetic resonance imaging system 302 is controlled with the pulse sequence commands 320 to acquire the magnetic resonance imaging data 322. Next in step 404 the multiple diffusion weighted images 112 are reconstructed from the magnetic resonance imaging data 322. After step 402 the method proceeds to steps 200-208 of the method illustrated in FIG. 2.

[0072] FIG. 5 shows several grids which represent a collection of multiple diffusion weighted images 112. In this example three diffusion weighted images 500, 502 and 504 are shown. These images are represented by grids. Each space in the grid represents one voxel. At a same location in each grid there is a voxel labeled 506. The voxel 506 is one of the corresponding voxels for the diffusion weighted images 500, 502 and 504. The set of equations is constructed using the intensity value for the voxel 506. This gives one set of equations which can be solved for b.sub.0. This process is then repeated for each of the other voxels in the diffusion weighted images 500, 502, 504.

[0073] Examples may provide for an improved Apparent Diffusion Coefficient (ADC) correction by correcting the image intensities of individual DWI images, without requiring an additional b.sub.0 Image. Even if an additional b.sub.0 image is acquired, a separate b.sub.0 can be computed using the where all DWI acquisitions (multiple diffusion weighted images) are included, typically this results in better SNR, less artefacts compared to the measured b.sub.0 image.

[0074] As mentioned above, in comparison to the Malyarenko paper examples skip the requirement of acquiring a non-diffused b.sub.0 image and still be able to correct for gradient non-linearity. This may allow for (somewhat) shorter scan-time and/or more flexibility in scan-protocols.

[0075] Another advantage is that a computed b.sub.0 estimate typically shows less noise and less artefacts than an acquired b.sub.0, potentially resulting in improved image quality of DWI scans where gradient non-linearity correction is applied.

[0076] A b0-like image 116 is estimated from a least-squares solution, assuming an exponential decay over the measured b-values, and such b.sub.0-like image is used in further calculations for gradient non-linearity corrections.

[0077] The Apparent Diffusion Coefficient (ADC) in gradient direction k, for a single pixel, is defined shown in Eq. 1 above.

[0078] Malyarenko disclosed a location r dependent correction map c.sup.k(r) to correct the image intensities:

[00001]$\begin{array}{cc}{S}_c\left(b^k,r\right)={S\left(0,r\right)}^{1-\frac{1}{c^k\left(r\right)}}.Math.{S\left(b^k,r\right)}^{\frac{1}{c^k\left(r\right)}}& \left(3\right)\end{array}$

[0079] The S(0,r) value is the b.sub.0 value at a particular location r (voxel location). S.sub.c(b.sup.k,r) is the corrected image intensity. S(b.sup.k,r) is the measured image intensity as is in Eq. 1. The location r dependent correction map c.sup.k(r) is a gradient nonlinearity correction.

[0080] The correction according to equation (3) requires a b.sub.0 image, however when multiple b-values are measured (which is a requirement for an ADC-map derivation), also a b.sub.0 can be estimated. Even if a b.sub.0 image is acquired, a b.sub.0 estimate can be computed from the multiple b-values. Typically, a b.sub.0 estimate shows less noise and less artifacts compared to a measured b.sub.0. As equation (3) shows the corrected image is a combination of a b.sub.0 and a b.sub.k image; thus, improving b.sub.0 improves the corrected image.

[0081] The b.sub.0 is estimated by performing a least-squares mono-exponential fit over the b-values (eq. (1)). As the measured tissue can be anisotropic, and the gradient non-linearity likely varies over the diffusion-directions, an ADC value per diffusion-direction is estimated. For a single pixel the linear equation we will optimize:

y=A.Math.x  (4)

[0082] Where vector y contains the natural logarithmic of all measured b-values and b-directions, A is the model matrix containing the b-values, and x is a vector containing the unknowns b.sub.0 and ADC values. Eq. (2) above can be used to set up Eq. 4.

[0083] For example, Eq. 4 can be re-written as:

[00002]$\begin{array}{cc}\ln \left(\begin{array}{c}S\left(0\right)\\ S\left(b_1^x\right)\\ S\left(b_1^y\right)\\ S\left(b_1^z\right)\\ S\left(b_2^x\right)\\ S\left(b_2^y\right)\\ S\left(b_2^z\right)\\ \mathrm{.Math.}\end{array}\right)=\left(\begin{array}{cccc}1& 0& 0& 0\\ 1& b_1^x& 0& 0\\ 1& 0& b_1^y& 0\\ 1& 0& 0& b_1^z\\ 1& b_2^x& 0& 0\\ 1& 0& b_2^y& 0\\ 1& 0& 0& b_2^z\\ 1& \mathrm{.Math.}& 0& 0\\ 1& 0& \mathrm{.Math.}& 0\\ 1& 0& 0& \mathrm{.Math.}\end{array}\right).Math.\left(\begin{array}{c}{b}_0\\ {\mathrm{ADC}}^x\\ {\mathrm{ADC}}^y\\ {\mathrm{ADC}}^z\end{array}\right),& \left(5\right)\end{array}$

where the superscripts b.sub.x,y,z denote orthogonal diffusion directions (not necessarily aligned with any axis, they can be oblique), and the subscripts b.sub.1,2 . . . denote the different b-values (or magnitudes as in (1)).

[0084] The first observation in Eq. (5) comes from a b.sub.0 acquisition, if a b.sub.0 is not acquired that observation can simply be discarded.

[0085] While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive; the invention is not limited to the disclosed embodiments.

[0086] Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word “comprising” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality. A single processor or other unit may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measured cannot be used to advantage. A computer program may be stored/distributed on a suitable medium, such as an optical storage medium or a solid-state medium supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems. Any reference signs in the claims should not be construed as limiting the scope.

LIST OF REFERENCE NUMERALS

[0087] 100 medical imaging system [0088] 101 computer [0089] 102 processor [0090] 104 hardware interface [0091] 106 user interface [0092] 108 memory [0093] 110 machine executable instructions [0094] 112 multiple diffusion weighted images [0095] 114 set of equations [0096] 116 b0 image [0097] 118 apparent diffusion coefficients [0098] 120 intensity corrected multiple diffusion weighted images [0099] 200 receive multiple diffusion weighted images of a subject [0100] 202 construct a set of equations for each of the at least one corresponding voxel [0101] 204 solve the set of equations for each voxel for the b0 value as an optimization [0102] 206 construct a b0 image using the b0 value for each voxel [0103] 208 calculate an image intensity correction of at least one of the multiple diffusion weighted images using the b0 image to correct for gradient non-linearity [0104] 300 medical imaging system [0105] 302 magnetic resonance imaging system [0106] 304 magnet [0107] 306 bore of magnet [0108] 308 imaging zone [0109] 309 region of interest [0110] 310 magnetic field gradient coils [0111] 312 magnetic field gradient coil power supply [0112] 314 radio-frequency coil [0113] 316 transceiver [0114] 318 subject [0115] 320 subject support [0116] 320 pulse sequence commands [0117] 322 magnetic resonance imaging data [0118] 400 control the magnetic resonance imaging system to acquire the magnetic resonance imaging data [0119] 402 reconstruct the multiple diffusion weighted images using the magnetic resonance imaging data [0120] 500 diffusion weighted image [0121] 502 diffusion weighted image [0122] 504 diffusion weighted image [0123] 506 voxel