JP2009056340A - Data regenerating method and apparatus, recording medium, data recording method, and recorder - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To analyze a diffusion tensor magnetic resonance image associated with a recording/regenerating method and apparatus and a recording medium. <P>SOLUTION: Diffusion weighted signals are acquired, each signal having a plurality of voxels (45). A quantity associated with the diffusion tensor is determined from the diffusion weighted signals (46). The quantity is preferably approximation of the diffusion tensor of the diffusion weighted signals. An empirical statistical distribution is determined for a quantity associated with the diffusion tensor (47). <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a recording / reproducing method and apparatus, and a recording medium.

(Cross-reference of related applications)
The following priority is claimed and is incorporated herein by reference. US Provisional Patent Application No. 60 / 135,427 filed May 21, 1999.

  The present invention relates to diffusion tensor magnetic resonance imaging (DT-MRI), and more particularly to analyzing DT-MRI signals using statistical properties of diffusion tensors.

  For the convenience of the reader, the following references describing the background of the present invention are listed and incorporated herein by reference. In the following, references are made to references by referring to reference numbers.

  The first demonstration of the measurement of diffusion tensor from more than 7 diffusion weighted echoes and the presentation of a formula relating the diffusion weighted signal and the diffusion tensor via the b matrix are presented below.

  (1) P.I. J. et al. Basser, J. et al. Mattiello, D.M. Le Bihan. Diagonal and off-diagonal components of the self-diffusion tenor: the relation to and estimation from the NMR spin-echo signal. 11th Annual Meeting of the SMRM, Berlin, 1992, p. 1222.

  The first demonstration of the measurement of the eigenvalues and eigenvectors of the diffusion tensor, its interpretation as the main diffusivity and main direction, and the concept of measurement of diffusion anisotropy and rotation invariance are presented below.

  (2) P.I. J. et al. Basser, D.M. Le Bihan. Fiber orientation mapping in an anisotropy medium with NMR diffusion spectroscopy. 11th Annual Meeting of the SMRM, Berlin, 1992, p. 1221.

  The first paper describing the calculation of the diffusion weighting factor needed to calculate the diffusion tensor from the measured diffusion weighted image is:

  (3) J. Org. Mattiello, P.M. J. et al. Basser, D.M. Le Bihan. Analytical expression for the b matrix in NMR diffusion imaging and spectroscopy. J. et al. Magn. Reson. A108, 131-141 (1994).

  The first summary describing the calculation of the diffusion weighting factor needed to calculate the diffusion tensor from the measured diffusion weighted image is:

  (4) J. Org. Mattiello, P.M. J. et al. Basser, D.M. Le Bihan. Analytical expressions for the gradient b-factor in NMR diffusion imaging. 12th Annual Meeting of the SMRM, New York, 1993, p. 1049.

  The following summary describes diffusion tensor magnetic resonance imaging.

  (5) P.I. J. et al. Basser, J. et al. Mattiello, D.M. Le Bihan. MR imaging of fiber-tract direction and diffusion in anisotropy tissues. 12th Annual Meeting of the SMRM, New York, 1993, p. 1403.

  (6) P.I. J. et al. Basser, J. et al. Mattiello, R.A. Turner, D.C. L. Bihan. Diffuse tenor echo-planar imaging of human brain. 12th Annual Meeting of the SMRM, New York, 1993, p. 1404.

  The following summary describes the b matrix format for DT-MRI.

  (7) J. Org. Mattiello, P.M. J. et al. Basser, D.M. Le Bihan. Analytical expressions for the b-matrix in diffusion tenor MR imaging. SMRM Worksshop: Functional MRI of the Brain, Arlington, VA, 1993, p. 223.

  The first published demonstration of DT-MRI is described below.

  (8) D. Le Bihan, P.A. J. et al. Basser, J. et al. Mattiello, C.I. A. Cuenod, S.M. Posse, R.A. Turner. Assessment of NMR diffusion measurements in biologic systems: effects of microdynamics and microstructure. Syllabus for: SMRM Workshop: Functional MRI of the Brain, Arlington, VA. 1993, p. 19-26.

  (9) P.I. J. et al. Basser, J. et al. Mattiello, R.A. Turner, D.C. L. Bihan. Diffusion tenor echo-planar imaging (DTPI) of human brain. SMRM Worksshop: Functional MRI of the Brain, Arlington, VA, 1993, p. 224.

  In the following, methodological issues with DT-MRI are described.

  (10) D.E. Le Bihan, P.A. J. et al. Basser. Molecular diffusion and nuclear magnetic resonance. In: Le Bihan D. ed. Diffusion and Perfusion Magnetic Resonance Imaging. New York: Raven Press, 1995: 5-17.

  (11) P.I. J. et al. Basser, D.M. Le Bihan, J .; Mattiello. Anisotropic diffusion: MR diffusion tenor imaging. In: LeBihan D. ed. Diffusion and Perfusion Magnetic Resonance Imaging. New York: Raven Press, 1995: 140-149.

  (12) J. et al. Mattiello, P.M. J. et al. Basser, D.M. Le Bihan. Analytical calculation of the b matrix in diffusion imaging. In LeBihan D.M. ed. Diffusion and Perfusion Magnetic Resonance Imaging. New York: Raven Press, 1995: 77-90.

  (13) J. Org. Mattiello, P.M. J. et al. Basser, D.M. Le Bihan. The b matrix in diffusion tenor echo-planar imaging. Magn Reson Med 37, 2, 292-300 (1997).

  The following discusses the demonstration of DT-MRI measurements of anisotropy in the monkey brain.

  (14) C.I. Pierpaoli, J. et al. Mattiello, D.M. Le Bihan, G.M. Di Chiro, P.A. J. et al. Basser. Diffusion tenor imaging of brain white matter anisotropy. 13th Annual Meeting of the SMRM, San Francisco, 1994, p. 1038.

  (15) I.I. Linfante, T.W. N. Chase, P.A. J. et al. Basser, C.I. Pierpaoli. Diffuse tenor brain imaging of MPTP-lesioned monkeys. 1994 Annual Meeting, Society for Neuroscience, Miami, FL, 1994.

  A method for calibrating the diffusion gradient using DT-MRI is presented below.

  (16) P.I. J. et al. Basser. A sensitive method to calibrate magnetic field gradients using the diffusion tenor. Third Meeting of the SMR, Nice, France, 1995, p. 308.

  The first paper describing the estimation of diffusion tensors from diffusion weighted signals or echoes is:

  (17) P.I. J. et al. Basser, J. et al. Mattiello, D.M. Le Bihan. Estimation of the effective self-diffusion tenor from the NMR spin echo. J. et al. Magn. Reson. B103, 3, 247-254 (1994).

  A description of MRI staining useful in tissue characterization is discussed below.

  (18) P.I. Basser, C.I. Pierpaoli. Elucidating Tissue Structure by Diffuse tenor MRI. SMR / ESMRMB, Nice, France, 1995, p. 900.

  A novel sequence for performing high speed and high resolution DT-MRI is presented below.

  (19) P.M. Jezard, C.I. Pierpaoli. Diffusing mapping using interleaved Spin Echo and STEAM EPI with navigator echo collection. SMR / ESMRMB Joint Meeting, Nice, 1995, p. 903.

  A demonstration of DT-MRI of the brain of a human subject is provided below.

  (20) C.I. Pierpaoli, P.M. Jezard, P.A. J. et al. Basser. High-resolution diffusion tenser imaging of the human brain. SMR / ESMRMB Joint Meeting, Nice, 1995, p. 899.

  (21) P.I. Jezard, C.I. Pierpaoli. Dual-Echo Navigator Approach to Minimization of Eddy Current and Motion Artifacts in Echo-Planar Diffusing Imaging. Proceedings of the ISMRM, New York, 1996, p. 189.

  Methods for using DT-MRI in transport and drug delivery applications are presented below.

  (22) P.I. G. McQueen, A.M. J. et al. Jin, C.I. Pierpaoli, P.M. J. et al. Basser. A Fine Element Model of Molecular Diffusion in Brain Incorporating in vivo Diffusion tenor MRI Data. Proceedings of the ISMRM, New York, 1996, p. 193.

  (23) C.I. Pierpaoli, B.M. Choi, P.A. Jezard, P.A. J. et al. Basser, G.M. Di Chiro. Significant changes in brain water diversity observed under hypersolar conditions. SMR / ESMRMB, Nice, France, 1995, p. 31.

  DT-MRI in an animal model of cerebral ischemia is presented below.

  (24) C.I. Pierpaoli, C.I. Baratti, P.M. Jezard. Fast Tensor Imaging of Water Diffusion Changes in Gray and White Matter Flowing Cardiac Arrest in Cats. Proceedings of the ISMRM, New York, 1996, p. 314.

  The first demonstration of secondary degeneration of nerve fibers in vivo following a stroke is presented below.

  (25) C.I. Pierpaoli, A.M. Banett, L.M. Penix, T .; De Graba, P.A. J. et al. Basser, G.M. Di Chiro. Identification of Fiber Generation and Organized Gliosis in Stroke Patents by Diffusion Tensor MRI. Proceedings of the ISMRM, New York, 1996, p. 563.

  The measurement of diffusion anisotropy has been proposed below.

  (26) C.I. Pierpaoli, P.M. J. et al. Basser. New Invant "Lattice" Index Achieves Significant Noise Reduction in Measuring Diffusion Anisotropy. Proceedings of the ISMRM, New York, 1996, p. 1326.

  A hierarchical statistical estimation model for improving diffusion tensor estimation is presented below.

  (27) P.I. J. et al. Basser. Testing for and exploiting microstructural symmetry to characterize tissue via diffusion tenor MRI, ISMRM, New York, 1996, p. 1323.

  The following are issued patents related to DT-MRI.

  (28) P.I. J. et al. Basser, J. et al. Mattiello, D.M. Le Bihan. Method and System for Measuring the Diffusion Tensor and for Diffusion Tensor Imaging. U.S. Pat. No. 5,539,310, issued July 23, 1996.

  Examples of the application of DT-MRI to developmental biology are presented below.

  (29) C.I. Barrati, A .; Barnett, C.I. Pierpaoli. Comparative MRI Study of Brain Measurement using T1, T2, and the Diffusion Tensor. 5th ISMRM, Vancouver, 1997, p. 504.

  Proof that at least seven diffusion weighted images are required to characterize the diffusion anisotropy is fully described below.

  (30) P.I. J. et al. Basser, R.A. Shrager. Anisotropically-weighed MRI. ISMRM Fifth Scientific Meeting, Vancouver, 1997, p. 226.

  (31) R.M. I. Shrager, P.A. J. et al. Basser. Anisotropically weighed MRI. Magn Reson Med 40, 1, 160-165 (1998).

  An error perturbation analysis and eigenvalues in the fiber direction are presented below.

  (32) P.I. J. et al. Basser. Quantifying Errors in Fiber Direction and Diffusion Tensor Field Map Resizing from MR Noise. 5th Scientific Meeting of the ISMRM, Vancouver, 1997, p. 1740.

  A simplified method for measuring the diffusion tensor is presented below.

  (33) P.I. J. et al. Basser, C.I. Pierpaoli. Analytical Expressions for the Diffusion Tensor Elements. 5th Annual ISMRM, Vancouver, 1997, p. 1738.

  (34) P.I. J. et al. Basser, C.I. Pierpaoli. A simplified method to measure the diffusion tenor from seven MR images. Magn Reson Med 39, 6, 928-934 (1998).

  A proposed method for estimating the eigenvalues of the diffusion tensor is given below.

  (35) P.I. J. et al. Basser, C.I. Pierpaoli. Estimating the Principal Differences (Eigenvalues) of the Effective Difference Tensor. 5th ISMRM, Vancouver, 1997, p. 1739.

  A demonstration of DT-MRI for diagnosing Pelizaeus-Merzbacher disease is given below.

  (36) C.I. Pierpaoli, B.M. Choi, R.A. Schiffmann, G.M. DiChiro. Diffusion Tensor MRI in Pelizaeus-Merzbacher Disease. 5th ISMRM, Vancouver, 1997, p. 664.

  The color mapping in the fiber direction obtained from DT-MRI data is presented below.

  (37) C.I. Pierpaoli. Oh No! One More Method for Color Mapping of Fiber Tract Direction Using Diffusion MR Imaging Data. 5th ISMRM, Vancouver, 1997, p. 1741.

  A scheme for following the neural fiber organ system using DT-MRI is presented below.

  (38) P.I. J. et al. Basser. Fiber-Tracography via Diffusion Tensor MRI (DT-MRI). 6th ISMRM, 1998, p. 1226.

  (39) P.I. J. et al. Basser. New histologic and physical stains derived from diffusion-tensor MR images. Ann NY Acad Sci 820, 123-138 (1997).

  A Monte Carlo method for simulating diffusion tensor MRI data is presented below.

  (40) C.I. Pierpaoli, P.M. J. et al. Basser. Toward a quantitative assessment of diffusion anisotropy. Magn Reson Med 36, 6, 893-906 (1996). Published erratum appears in Magn Reson Med June 1997: 37 (6): 972.

  The first paper describing DT-MRI in normal human subjects is presented below.

  (41) C.I. Pierpaoli, P.M. Jezard, P.A. J. et al. Basser, A.M. Barnett, G.M. Di Chiro. Diffusion tenor MR imaging of the human brain. Radiology 201, 3, 637-648 (1996).

  Diffusion anisotropy and texture measurements are presented below.

  (42) P.I. J. et al. Basser, C.I. Pierpaoli. Microstructural and physical features of tissues elaborated by quantitative-diffusion-tensor MRI. J Magn Reson B 111,3,209-219 (1996).

  The diffusion tensor MRI “stain” is presented below.

  (43) P.I. J. et al. Basser. Infraring microstructural features and the physical state of tissues from weight diffusion-weighted images, NMR Biomed 8, 7-8, 333-344 (1995).

  The first paper describing DT-MRI is:

  (44) P.I. J. et al. Basser, J. et al. Mattiello, D.M. Le Bihan. MR diffusion tenser spectroscopy and imaging. Biophys J 66, 1, 259-267 (1994).

  The application of gradient patterns for DT-MRI is discussed below.

  (45) T.W. L. Davis, v. J. et al. Weeden, R.A. M.M. Weisskoff, B.M. R. Rosen. White matter tract visualization by echo-plan MRI. SMRM Twelfth Annual Meeting, New York, NY, 1993, p. 289.

  A description of nuclear magnetic resonance (NMR) noise is provided below.

  (46) H.M. Gudbjartsson, S.M. Patz. The Rician distribution of noisy MRI data [published erratum appears in Mag Reson Med August 1996; 36 (2): 332], Magnet Reson Med 34, 6, 910-9.

  (47) R.M. M.M. Henkelman. Measurement of signal intensities in the presence of noise in MR images. Med. Phys. 12, 2, 232-233 (1985).

  The bootstrap method is discussed below.

  (48) Efron B.E. "Bootstrap methods: Another look at the jackknife", Ann. Statist. , Vol7, pp1-26.

  Several statistical issues related to interpreting DT-MRI data are discussed below.

  (49) S.M. Pajevic, and P.P. J. et al. Basser. Parametric Description of Noise in Diffusion Tensor MRI. 8th Annual Meeting of the ISMRM, Philadelphia, 1787 (1999).

  (50) S.M. Pajevic, and P.P. J. et al. Basser. Non-parametric Statistical Analysis of Diffusion Tensor MRI Data Using the Bootstrap Method. 8th Annual Meeting of the ISMRM, Philadelphia, 1790 (1999).

  Problems with multivariate statistics applied to DT-MRI data are discussed below.

  (51) T.M. W. Anderson. An Introduction to Multivariate Statistics: John Wiley & Sons, 1984.

  Computer code that implements an algorithm for performing statistical tests is discussed below.

  (52) W.M. H. Press, S.M. A. Teukolsky. W. T.A. Vetterling, B.W. P. Flannery. Numeric Recipes in C.I. Cambridge: Cambridge University Press, 1992.

  Other clinical and methodological aspects of DT-MRI are provided below.

  (53) P.I. van Gelderen, M.M. H. M.M. d. Vleeschouwer, D.C. DesPres, J.A. Pekar, P.M. C. M.M. v. Zijl, C.I. T.A. W. Moonen. Water Diffusion and Accu Stroke. Magnetic Resonance in Medicine 31, 154-163 (1994).

  (54) A. M.M. Ulug, N .; Beauchamp, R.A. N. Bryan, and P.M. C. M.M. van Zijl, Absolute Quantification of Diffusion Constants in Human Stroke, Stroke 28, 483-490 (1997).

  (55) M.M. E. Bastin, M.M. del Grado, I.D. R. White, and J.M. M.M. Wardlaw. An Investigation into the Effect of Dexamethasone on Intracerebral Tumors using MR Diffuse Tensor Imaging, ISMRM, 902 (1999).

  (56) P.I. Mukherjee, M.M. M.M. Bahn, R.A. C. McKinstry, J.M. S. Shimony, T .; S. Cull, E .; Akbudak, A .; Z. Snyder, and T.M. E. Conturo. Differences in Water Difficulty Between Gray Matter and White Matter in Stroke: Diffusion Tensor MR Imaging Experience in TwelvePet.

  (57) M.M. A. Horsfield, M.M. Lai, S .; L. Webb, G .; J. et al. Barker, P.M. S. Tofts, R.M. Turner, P.M. Rudge, and D.C. H. Miller. Applicable diffusion coefficients in benign and secondary progressive multiple sclerosis by nuclear magnetic resonance. Magn. Reson. Mod. 36 3,393-400 (1996).

  (58) M.M. A. Horsfield, H.C. B. Larsson, D.C. K. Jones, and A.J. Gass. Diffuse magnetic resonance imaging in multiple sclerosis. J Neurol Neurosurg Psychiatry 64 Suppl 1, S80-84 (1998).

  (59) A.1. O. Nusbaum, C.I. Y. Tang, M.M. S. Buchsbaum, L.M. Shihabuddin, T .; C. Wei, and S.W. W. Atlas. Regional and Global Differences in Cerebral White Matter Diffusion with Alzheimer's Dissease, ISMRM, Philadelphia, 956 (1999).

  (60) R.M. Turner, and D.C. Le Bihan. Single shot diffusion imaging at 2.0 Tesla, J. et al. Magn. Reson. 86, 445 to 452 (1990).

  (61) J. et al. H. Simpson, and H.M. Y. Carr. Diffusion and nuclear spin relaxation in water. Physical Review 111 5, 1201-1202 (1958).

  (62) H.I. Y. Carr, and E.M. M.M. Purcell. Effects of diffusion on free precession in nuclear magnetic resonance experiments. Phys. Rev. 94 3,630-638 (1954).

  Techniques for determining the average ADC are discussed below.

  (63) G. Liu, P.A. van Gelderen, C.I. T.A. W. Moonen. Single-Shot Diffusion MRI on a Conventional Clinical Instrument. Second SMR Meeting, San Francisco, 1994, p. 1034.

  (64) T.W. E. Conturo, R.A. C. McKintry, E .; Akbudak, B.M. H. Robinson. Encoding of anisotropy diffusion with tetrahedral gradients: a general mathematical diffusion formalism and experimental results. Magn Reson Med 35, 3, 399-412 (1996).

  (65) S.M. Mori, P.M. C. van Zijl. Diffusing weighting by the trace of the diffusion tenor with a single scan. Magn. Reson. Med. 33, 1, 41-52 (1995).

  (66) E.E. C. Wong, R.A. W. Cox. Single-shot Imaging with Isotrophic Diffusing Weighting. Second Annual Meeting of the SMR, San Francisco, 1994, p. 136.

  (67) E.E. C. Wong, R.A. W. Cox, A.M. W. Song. Optimized isotrophic diffusion wetting. Magn Reson Med 34, 2, 139-143 (1995).

The effective diffusion tensor D (or D ^eff ) of water, measured via diffusion tensor magnetic resonance imaging (DT-MRI), is sensitive to tissue structure and its changes in disease, growth, aging, etc. is there. However, there is noise in these D measurements. At present, it is not well known what probability distribution describes the variability of D. Therefore, it was not possible to establish quantitatively whether the observed changes or fluctuations in D were statistically significant. The inventor found that in an ideal experiment D is described by a multivariate Gaussian (or normal) distribution and determines the statistical significance of the observed change in D (and the amount derived from it). Quantitative hypothesis tests to develop and techniques to report these data using generally understood and well-established statistical methods. Second, since the statistical distribution of D is now well known from the present invention, it can be determined whether DT-MRI data has been compromised by systematic artifacts that deviate the distribution from normality.

  The present invention now makes DT-MR imaging and spectral data more useful because the reliability of DT-MR imaging and spectral data can now be evaluated. Clinically, this new information can be used to diagnose stroke (both acute and chronic) and to identify ischemic “penumbra”. Advantageously, the present invention can be used to evaluate soft tissue and muscle structure in orthopedic and cardiology applications. Advantageously, the present invention can be used in neonatal screening and diagnostic applications. In general, advantageously, the present invention can segment, cluster and classify them based on the diffusion characteristics of different tissue types. In the present invention, advantageously, this information can improve research to screen for the efficacy of newly discovered drugs. The present invention can reduce the cost of clinical trials and the time required to perform clinical trials by reducing the number of patients and identifying inappropriate subjects. Advantageously, the present invention can be used to provide quantitative support for the safety and efficacy claims necessary to obtain FDA approval for drugs, medical devices, and tissue engineering products. . In phenotype / genotype studies at laboratories and pharmaceutical companies, these improved imaging parameters obtained with the present invention determine the phenotypic alterations in the histology and the architecture for a given genotype transient mutation Can help. Advantageously, the information gained from the present invention can help material engineers develop new and processed materials (eg, polymers, thin films, gels, plastics, coatings, etc.) and qualify their quality. it can.

  In addition, the present invention includes a novel use or variation of the nonparametric bootstrap method to generate a second or higher moment estimate of the diffusion tensor and its function in each voxel. The non-parametric method used in the present invention is a technique for generating a probability distribution of diffusion tensor data using a set of empirical diffusion weighted images (eg, acquired during a single patient scanning session). From this probability distribution, the moments and other characteristics of the probability distribution can be determined. This aspect of the invention makes it possible to test the integrity of the empirical diffusion tensor data in each voxel. This is because the absence of systematic artifacts indicates that the distribution of the diffusion tensor is statistically normal. Thus, statistically significant deviations from normality are evidence of phylogenetic artifacts in DT-MRI data. Finally, this approach is useful for empirical design of DT-MR imaging and spectroscopic experiments.

  Once the diffusion tensor is estimated for each voxel, the voxels can also be grouped into the region of interest (ROI). The distribution of the elements of the diffusion tensor within the ROI or a distribution of quantities that are a function of the elements of the diffusion tensor is also calculated. A statistical hypothesis test is then applied to determine if there is a significant difference between tissues in different ROIs, for example in disease diagnosis applications, or observed at different times, for example in long-term studies It is determined whether there are any differences between tissues within the same ROI.

  The present invention can be implemented as a method, an apparatus, and an article of manufacture.

  The method of the present invention includes analyzing a diffusion tensor magnetic resonance signal to obtain a plurality of diffusion weighted signals, each signal having a plurality of voxels, and a plurality of diffusion weighted signals. Sampling and obtaining at least one set of resampled diffusion weighted signals; determining a per-voxel diffusion tensor from each set of resampled diffusion weighted signals; and from at least one set of resampled diffusion weighted signals Determining an empirical statistical distribution of quantities associated with the diffusion tensor from the determined diffusion tensor. The empirical statistical distribution can then be used to diagnose the subject used to generate the diffusion weighted signal.

  The method of the present invention includes analyzing a diffusion tensor magnetic resonance signal, obtaining a plurality of diffusion weighted signals, each signal having a plurality of voxels, and at least two attentions in the signal. Each region of interest has at least one voxel; determining a diffusion tensor for each voxel in each region of interest from a diffusion weighted signal; and Determining an empirical statistical distribution of quantities associated with the diffusion tensor from the diffusion tensor for each voxel in the region. The empirical statistical distribution can then be used to diagnose the subject used to generate the diffusion weighted signal.

  Further, the method of the present invention includes analyzing a diffusion tensor magnetic resonance signal, obtaining a plurality of diffusion weighted signals for a first time point, each signal having a plurality of voxels; A step of identifying a region of interest in a diffusion weighted signal for one time point, the step of the region of interest having at least one voxel, and a region of interest for the first time point from the diffusion weighted signal for the first time point Determining a diffusion tensor for each voxel in; determining from the diffusion tensor for each voxel in the region of interest for the first time point; determining an empirical statistical distribution of quantities associated with the diffusion tensor; Obtaining a plurality of spreading weighted signals, each signal having a plurality of voxels , Identifying a region of interest in the diffusion weighted signal for the second time point, the region of interest having at least one voxel, and the attention to the second time point from the diffusion weighted signal for the second time point. Determining a diffusion tensor for each voxel in the region to be determined, and determining an empirical distribution for the amount associated with the diffusion tensor from the diffusion tensor for each voxel in the region of interest for the second time point. The empirical statistical distribution can then be used to diagnose the subject used to generate the diffusion weighted signal.

  Further, the method of the present invention includes analyzing a diffusion tensor magnetic resonance signal, obtaining a plurality of diffusion weighted signals, each signal having a plurality of voxels, and from the diffusion weighted signal. Determining a quantity associated with a diffusion tensor for each voxel and determining an empirical statistical distribution for the quantity associated with the diffusion tensor from the quantity associated with the diffusion tensor. The empirical statistical distribution can then be used to diagnose the subject used to generate the diffusion weighted signal.

  The apparatus according to the present invention includes a computer programmed with software for operating the computer according to the method of the present invention.

  The product relating to the present invention includes a computer readable medium for implementing software to control a computer to perform the method of the present invention.

  “Computer” refers to any device that can accept structured input, process the structured input according to predetermined rules, and generate the result of the processing as output. Examples of computers include computers, general purpose computers, supercomputers, mainframes, superminicomputers, minicomputers, workstations, microcomputers, servers, interactive televisions, and hybrid combinations of computers and interactive televisions. . A computer also refers to two or more computers connected via a network to send and receive information between the computers. Examples of such computers include distributed computer systems for processing information via computers linked by a network.

  “Computer-readable medium” refers to any storage device used to store data accessible to a computer. Examples of computer readable media include computer readable electronic data such as magnetic hard disks, floppy disks, optical disks such as CD-ROMs, magnetic tapes, memory chips, and carrier waves used in sending and receiving e-mails or accessing networks. The carrier used to carry the is included.

  “Computer system” refers to a system having a computer. However, the computer includes a computer-readable medium that causes software to operate the computer.

  “Network” refers to a number of computers and associated devices that are connected by a communication function. The network includes permanent connections, such as cables, or temporary connections, such as connections created over telephones or other communication links. Examples of networks include the Internet, such as the Internet, an intranet, a local area network (LAN), a wide area network (WAN), and a combination of networks such as the Internet and an intranet.

  Furthermore, the above objects and advantages of the present invention are illustrative and are not exhaustive of what can be achieved by the present invention. Accordingly, both these and other objects of the invention realized herein, as well as these and other objects of the invention as modified in light of any variation that would be apparent to one skilled in the art, are described herein. It will be clear from

(table of contents)
1. 1. Analysis of DT-MR signal 2. Parametric description of noise with diffusion tensor MRI 2.1 Overview 2.2 Method 2.3 Results and discussion 3. Nonparametric statistical analysis of diffusion tensor MRI data using bootstrap method 3.1 Overview 3.2 Method 3.3 Results and discussion 4. Bootstrap analysis of DT-MRI data 4.1 Overview 4.2 Method 4.3 Results and discussion 5. Quantitative statistical tests to assess changes in diffusion tensor traces: clinical and biological implications 5.1 Overview 5.2 Methods 5.3 Results and Discussion Quantitative test for trace variability of the apparent diffusion tensor of water: clinical and biological implications 6.1 Overview 6.2 Method 6.3 Results and Discussion

(1. Analysis of DT-MR signal)
FIG. 1 shows a flowchart for analyzing a DT-MR signal. Details of the flow diagram of FIG. 1 are discussed in the following sections.

  At block 10, a spreading weighted signal is acquired, each signal including a number of voxels. Preferably, each signal includes at least one voxel. The diffusion weighted signal is obtained by a measurement technique. Preferably, the diffusion weighted signal is based on the subject's measurements, and the subject is either living or non-living. Examples of organisms are humans and animals. Non-living examples are phantoms, dead humans, dead animals, polymers, thin films, gels, plastics, and coatings. Alternatively, the diffusion weighted signal can also be obtained from simulation using a computer and software. Alternatively, the diffusion weighted signal is stored and read on a computer readable medium.

  At block 11, the spread weighted signal is sampled to obtain at least one set of resampled spread weighted signals. Preferably, this resampled diffusion weighted signal is used in bootstrap simulation. This bootstrap simulation is discussed in more detail below. Preferably, the diffusion weighted signal is a diffusion weighted image.

  At block 12, a diffusion tensor is determined for each voxel from each set of resampling diffusion weighted signals. Techniques for determining the diffusion tensor are well known. Preferably, resampling is performed multiple times.

  Optionally, a diffusion tensor can be determined for each voxel in the subset of voxels of the resampled diffusion weighted signal. This subset can be referred to as a region of interest (ROI). The number of voxels in the ROI can be at most the number of voxels in the resampled spread weighted signal and can be at least one voxel in the resampled spread weighted signal.

  Optionally, a diffusion tensor can be determined for each voxel in at least one subset of the voxels of the resampled diffusion weighted signal. This subset can be referred to as a region of interest (ROI). The number of voxels in each ROI can be at most the number of voxels in the resampled spread weighted signal and can be at least one voxel in the resampled spread weighted signal.

  At block 13, an empirical statistical distribution is determined with respect to a quantity associated with the diffusion tensor. Preferably, the empirical statistical distribution is determined using non-parametric techniques, such as the bootstrap method discussed further below. Other non-parametric techniques such as empirical resampling schemes can also be used. Preferably, the empirical statistical distribution is at least one of a probability density function, a cumulative density function, and a histogram. Preferably, the quantity associated with the diffusion tensor is at least one of a diffusion tensor element, a linear combination of diffusion tensor elements, and a diffusion tensor function. Preferably, the linear combination of elements of the diffusion tensor is a trace of the diffusion tensor. Other empirical distributions and associated quantities can also be determined.

  In block 14, the subject is diagnosed based on this amount of empirical statistical distribution. Preferably, the subject is diagnosed based on the characteristics of the empirical statistical distribution for this quantity. Preferably, the empirical statistical distribution is either a probability density function or a cumulative density function, and the empirical statistical distribution features are first and higher order moments of the empirical statistical distribution.

  Optionally, the subject can be diagnosed by segmenting, clustering, or classifying portions of the subject based on features of the empirical statistical distribution for this quantity.

  Optionally, systematic artifacts in the subject's diffusion weighted signal can be identified based on the characteristics of the empirical statistical distribution for this quantity. Preferably, the empirical statistical distribution for this quantity is compared with the parametric statistical distribution for this quantity to identify systematic artifacts. For example, the parametric distribution can be a multivariate Gaussian distribution in which this quantity is a diffusion tensor. As another example, the parametric distribution can be a univariate Gaussian distribution whose quantity is a trace of the diffusion tensor.

  In block 12 of FIG. 1, a diffusion tensor is determined for each voxel in the diffusion weighted signal or for a voxel of a subset of voxels in the diffusion weighted signal. This subset can be referred to as a region of interest. Optionally, the diffusion tensor can be determined for two or more subsets of voxels in the diffusion weighted signal. Here, this subset is called a region of interest. FIG. 2 illustrates this concept as a flowchart for analyzing DT-MR signals for at least two regions of interest. Details of the flow diagram of FIG. 2 are discussed in the following sections.

  In block 20, a spreading weighted signal is acquired, each signal having a voxel. Preferably, each signal includes at least one voxel. Block 20 is similar to block 10.

  At block 21, the diffusion weighted signal is sampled to obtain at least one set of resampled diffusion weighted signals. Block 21 is similar to block 11.

  At block 22, at least two regions of interest (ROI) in the resampled spread weighted signal are identified. However, each ROI includes at least one voxel.

  At block 23, a diffusion tensor is determined for each voxel in each ROI from the resampled diffusion weighted signal. Block 23 is similar to block 12 except that the diffusion tensor is determined in at least two ROIs.

  At block 24, an empirical statistical distribution is determined from the diffusion tensor for each voxel in each ROI with respect to the quantity associated with the diffusion tensor. Block 24 is similar to block 12 except that the diffusion tensor is determined with respect to at least two ROIs.

  At block 25, the empirical statistical distribution for this quantity is compared across ROIs to obtain differences in the characteristics of the empirical statistical distribution for quantities between ROIs. Preferably, the difference in the empirical statistical distribution feature for this quantity is determined by performing a hypothesis test on the difference in the empirical statistical distribution characteristic for this quantity between the regions of interest. In addition, an analysis similar to that described for block 14 can be performed for the ROI at block 25.

  In FIG. 1, the flow chart is for a single point in time. As an option, the flow diagram of FIG. 1 may be performed for more than one time point for a subject. For example, if the subject is a human and the person has a stroke, the flow chart of FIG. 1 can be performed as the first time point immediately after the onset of the stroke, and then as the second time point approximately one month later. The results for the first time point and the second time point can then be compared and the differences in humans over time can be analyzed. Additional time points can be obtained for further comparison and analysis. FIG. 3 illustrates this concept as a flow chart for analyzing the DT-MR signal for the first time point and the second time point. This technique can be modified to include additional time points. Details of the flow diagram of FIG. 3 are discussed in the following section.

  At block 30, a spreading weighted signal for the first time point is obtained, each signal including a voxel. Preferably, each signal includes at least one voxel. Block 30 is similar to block 10 except for the first time point.

  At block 31, the spreading weighted signal for the first time point is sampled to obtain at least one set of resampled spreading weighted signals for the first time point. Block 31 is similar to block 11 except for the first time point.

  At block 32, the ROI of the resampled diffusion weighted signal for the first time point is identified. However, this ROI includes at least one voxel. The number of voxels in the ROI can be up to the number of voxels in the resampling diffusion weighted signal, and can be a minimum of 1 voxel.

  At block 33, a diffusion tensor is determined for each voxel in the ROI from the resampled diffusion weighted signal for the first time point. Block 33 is similar to block 12 except for the first time point.

  At block 34, an empirical statistical distribution is determined with respect to an amount associated with the diffusion tensor for the first time point. Block 34 is similar to block 13 except for the first time point.

  At block 35, a spreading weighted signal for the second time point is obtained, each signal including at least one voxel. Preferably, each signal includes at least one voxel. Block 35 is similar to block 30 except for the second time point.

  At block 36, the spreading weighted signal for the second time point is sampled to obtain at least one set of resampled spreading weighted signals for the second time point. Block 36 is similar to block 31 except for the second time point.

  At block 37, the ROI of the resampled diffusion weighted signal for the second time point is identified. However, this ROI includes at least one voxel. The number of voxels in the ROI can be up to the number of voxels in the resampling diffusion weighted signal, and can be a minimum of 1 voxel. Preferably, approximately the same ROI is identified in blocks 32 and 37.

  At block 38, a diffusion tensor is determined for each voxel in the ROI from the resampled diffusion weighted signal for the second time point. Block 38 is similar to block 33 except for the second time point.

  At block 39, an empirical statistical distribution is determined with respect to an amount associated with the diffusion tensor for the second time point. Block 39 is similar to block 34 except for the second time point.

  At block 40, the characteristics of the empirical statistical distribution are compared with respect to the quantity for at least one ROI between the first time point and the second time point. By comparing empirical statistical distributions for two different time points, changes in time can be monitored and analyzed. In addition, an analysis similar to that described with respect to block 14 can be performed for the two time points at block 40.

  After first determining the diffusion tensor in block 12 of FIG. 1, an empirical statistical distribution of the quantity associated with the diffusion tensor is determined in block 13 of FIG. Optionally, for some quantities associated with the diffusion tensor, it may not be necessary to first determine the diffusion tensor as in block 21. FIG. 4 illustrates this concept as a flow diagram for analyzing a DT-MR signal without determining a diffusion tensor. Details of the flow diagram of FIG. 4 are discussed in the following section.

  At block 45, a spreading weighted signal is acquired, each signal including a number of voxels. Preferably, each signal includes at least one voxel. Block 45 is similar to block 10.

  At block 46, an amount associated with the diffusion tensor of the diffusion weighted signal is determined from the diffusion weighted signal. Preferably, this amount is an approximation of the diffusion tensor trace of the diffusion weighted signal. As discussed further below, Trace (D) can be approximated using a total of 5, 4, 2, or one diffusion weighted image.

  At block 47, an empirical statistical distribution is determined for the quantity associated with the diffusion tensor. Block 47 is similar to block 13.

  At block 48, the subject is diagnosed based on this amount of empirical statistical distribution. Block 48 is similar to block 14.

  Optionally, the technique of FIG. 4 can be used in combination with the technique of FIG. 2 to analyze one or more ROIs.

  Optionally, the technique of FIG. 4 can be used in combination with the technique of FIG. 3 to analyze two or more time points.

(2. Parametric description of noise in diffusion tensor MRI)
In this section, an ideal parametric model for describing noise in DT-MRI experiments is established as a multivariate normal distribution.

(2.1 Overview)
It is well known that the background noise characteristics of an amplitude MRI image are conformal to the Ricean distribution (46), (47). In diffusion tensor magnetic resonance imaging (DT-MRI), the components of a diffusion tensor are estimated from a noisy diffusion weighted (DW) amplitude image using regression analysis, usually linear regression of a log-linearized DW amplitude signal. (17). So far, there has been no attempt to characterize the statistical distribution of diffusion tensor data. This study reveals the noise characteristics of the diffusion tensor data, assuming that the amplitude image is a Rician distribution.

  For signal-to-noise (S / N) ratios greater than 3, the Rician distribution is the mean

And a normal distribution with a variance σ ² that is the variance of the signal in each quadrature channel. The relationship between the amplitude of the NMR signal and the diffusion tensor component is non-linear. Therefore, it is difficult to reach an analytical expression regarding the noise distribution of the diffusion tensor element. However, since regression analysis is usually performed using a large number of independent signals, the distribution of diffusion tensor elements is expected to be a Gaussian distribution by the central limit theorem even for a small S / N ratio.

(2.2 Method)
Diffusion tensor data was generated using Monte Carlo simulation by assuming that the noise in the amplitude image is described by a Rician distribution. Different types of diffusion processes were modeled. Isotropic and anisotropic diffusion tensors that cover typical values obtained in a living human brain were used. Again, a wide range of S / N values (1-100) and imaging parameters were searched (eg, the number of images acquired for regression ni was 7 to 70). Actual DT-MRI experiments obtained from healthy female volunteers to test for normality of diffusion tensor values in different regions of the brain using the Kolmogorov-Smirnov (KS) test with p = 0.01 Data was used.

(2.3 Results and discussion)
Using the Monte Carlo simulation of the DW-MRI experiment, the six independent components of D ^eff (written as a 6-dimensional vector) are distributed according to a multivariate Gaussian distribution. This is true even if the S / N is less than 2 and only 7 images are used for regression. This distribution consists of two 6-dimensional mean vectors μ = {μ _xx , μ _yy , μ _zz , μ _xy , μ _xz , μ _yz } and a 6 × 6 covariance matrix Σ having non-zero diagonal elements. Described by parameters. This multivariate distribution for the vector x = {D _xx , D _yy , D _zz , D _xy , D _xz , D _yz } is written as:

If a region of interest (ROI) with a uniform tensor value can be found, estimates of μ and Σ are obtained directly. Empirically, the estimation of the sample covariance matrix was obtained using bootstrap analysis or the Monte Carlo method, and analytically using the linear regression model (17). Linear model estimation for log-linearized data is biased for low S / N, specifically for the variance of the diagonal elements of the tensor. Again, when the signal reaches the background noise level, the prediction of Σ decreases for high diffusion attenuation (eg, large Trace ( b )). Based on experiments on isotropic diffusion of water, the diffusion tensor component follows a Gaussian distribution. When testing the normality of patient data, it was found that the majority of voxels conform to a normal distribution. However, for some, the distribution deviates significantly from normality according to the Kolmogorov-Smirnov test. In this case, the off-diagonal elements are more likely to deviate from the normal distribution than the diagonal elements. These may usually be type 1 errors for the Kolmogorov-Smirnov test, but deviations from these normalities are attributed to motion and other phylogenetic artifacts that are excluded in the Rician noise model and are not described parametrically. difficult. This suggests a method for testing for such artifacts by testing diffusion tensor data for normality.

FIG. 5 shows the probability distribution of six independent components of an effective diffusion tensor obtained from Monte Carlo simulations, namely anisotropic D ^eff components. This average vector is μ = {1104,661,329,180,135,77} μm ² / s. The solid line shows the fit to the Gaussian distribution.

(3. Nonparametric statistical analysis of diffusion tensor MRI data using the bootstrap method)
(3.1 Overview)
Applications of diffusion tensor magnetic resonance imaging (DT-MRI) have developed significantly in recent years. Calculate other rotational invariant measurements from the measured diffusion tensor D ^eff , such as the main diffusivity, diffusion tensor trace, Trace ( D ^eff ), relative anisotropy, and other histological staining Can do. Currently, only the average value or first-order moment of these quantities can be estimated for each voxel. Knowing these quantities of uncertainty or higher-order moments, and their probability distributions, helps improve the ability to design DT-MRI experiments more efficiently and analyze DT-MRI data.

  In the previous section, we established a multivariate Gaussian distribution as an appropriate parametric statistical model for diffusion tensor data. However, this is only true when there are no movements and other systematic artifacts that are difficult to describe parametrically. Therefore, the present invention uses the bootstrap method (48) as a general technique for analyzing DT-MRI data. This bootstrap method is an empirical non-parametric resampling technique to obtain estimates of standard error, confidence intervals, probability distributions, and other measurements of uncertainty. The bootstrap sample is used to infer the characteristics of the sample in the same way that a normal sample is used to infer the statistical characteristics of the population. The applicability of the bootstrap method to DT-MRI is demonstrated and the limitations of the data bootstrap method are evaluated using empirical DT-MRI data and data synthesized using Monte Carlo simulation.

(3.2 Method)
The effective diffusion tensor D ^eff is estimated by applying a magnetic field gradient in at least six oblique directions specified by the symmetric matrix b . D ^eff is estimated from b and the measured T ₂ weighted signal using weighted multivariate linear regression (17), where T2 weighted signal A (0) without diffusion weighting is also estimated. . A Monte Carlo simulation of the DT-MRI experiment was performed (40). Monte Carlo simulations were used to obtain a set of n noisy signals per diagonal direction and n signals using zero / small magnetic field gradient, for a total of 7n signals. This is called the original set. The original set is used to create a bootstrap set by taking n random samples (with replacement) from each of the seven sets and obtaining a “new” set of 7n signals. By repeating this step many times, N _B times, many estimates are obtained for each D ^eff along with other quantities of interest, such as diffusion tensors, Trace ( D ^eff ), eigenvalues, eigenvectors, and the like. A “true” distribution of these quantities can also be predicted using Monte Carlo simulations to validate the bootstrap results.

(3.3 Results and discussion)
Error and probability distribution estimates were calculated for various quantities of interest. Bootstrap standard error (SE) is a non-parametric maximum likelihood estimate of true SE. It has been found that the bootstrap method is particularly suitable for DT-MRI measurements because a reliable estimate of the error for a single voxel can be obtained within a non-uniform region. This information cannot be obtained using conventional techniques. This is because only n samples can be used to estimate the SE (n is generally less than 5). When estimating errors using voxels in the ROI, the SE is greatly exaggerated due to non-uniformities in the ROI. For example, an ROI consisting of 15 voxels taken from around a particular voxel in gray matter but very close to the CSF (empirical DT-MRI data at n = 4) is for the tensor component D _xx Standard deviation σ = 271 μm ² / s.

FIG. 6 shows a probability distribution of D _xx in the ROI obtained using bootstrap analysis. This probability distribution indicates the presence of different modes. The bootstrap estimate of the probability distribution for D _xx is for n = 4 and N _B = 5000. The ROI is in the gray matter but is taken from near the CSF, so partial volume artifacts can be seen.

FIG. 7 shows the probability distribution of D _xx obtained within a single voxel. A probability distribution of D _xx is obtained within a single voxel in gray matter using bootstrap analysis. This probability distribution fits very well to a Gaussian distribution with σ = 75 μm ² / s and is much smaller and more appropriate than ROI estimation. The validity of the bootstrap method was confirmed using real data and Monte Carlo simulation.

This bootstrap method facilitates the use of many new statistical techniques for designing and analyzing DT-MRI. The inventor provides an estimate of uncertainty and the probability distribution of measured and calculated variables in DT-MRI, booting, provided that a sufficient number of images are used in a bootstrap resampling scheme. We have found that it can be obtained using strap analysis. Bias, outliers, and confidence levels can also be obtained using the bootstrap method, and hypothesis testing can also be performed using the bootstrap method. The main disadvantage of the bootstrap method is that it requires a longer calculation time, the calculation time is proportional to N _B. For example, for N _B = 1000, the bootstrap analysis takes about 0.5 seconds per voxel on a SPARC ULTRA-60 workstation. However, on parallel computers, the bootstrap method can be implemented more efficiently. Overall, the bootstrap method is an effective tool for statistical analysis of DT-MRI data.

(4. Bootstrap analysis of DT-MRI data)
(4.1 Overview)
In DT-MRI, the average value of diffusion tensor components is estimated using statistical methods such as regression. Using these measured tensor components, other rotation invariant measurements such as main diffusivity, diffusion tensor trace, Trace ( D ^eff ), and relative anisotropy can be calculated. At present, only an average value or first moment is estimated for each voxel. However, knowing the uncertainty or higher order moments of these quantities, and their probability distributions, helps to design DT-MRI experiments more efficiently and also improves the analysis of DT-MRI data. Obtaining a theoretical estimate of standard error or a probability distribution of a given statistic is complicated because parametric models are not well known and many of the derived quantities are nonlinear functions of diffusion tensor components.

  The present invention uses a novel application of the bootstrap method (48). This bootstrap method is an empirical non-parametric resampling technique to obtain estimates of standard error, confidence intervals, probability distributions, and other measurements of parameter uncertainty. This bootstrap method is applied to DT-MRI, and the limitations of this method are evaluated using empirical DT-MRI data and data synthesized using Monte Carlo simulation.

(4.2 Method)
The effective diffusion tensor D ^eff is estimated by applying a magnetic field gradient in at least six diagonal directions specified by the symmetric matrix b . From b and the measured T ₂ weighted signal, D ^eff is estimated using weighted multivariate linear regression (17), where A (0) is also estimated. A Monte Carlo simulation of the DT-MRI experiment was performed (40). Monte Carlo simulation techniques were used to obtain a set of n noisy signals per diagonal direction and n signals using zero / small magnetic field gradient, for a total of 7n signals. This is called the original set. The original set is used to create a bootstrap set by taking n random samples (with permutations) from each of the seven sets and obtaining a “new” set of 7n signals. Many times this step, by repeating N _B times, the amount of other interest, for example, with a diffusion tensor deviation eigenvectors to obtain a number of estimates of the D ^eff. Although the computation time is proportional to the number N _B , the bootstrap method can be implemented more efficiently on a parallel computer. A “true” distribution can also be predicted using Monte Carlo simulations to validate the bootstrap results.

(4.3 Results and discussion)
Probability distributions were calculated for various quantities of interest. FIG. 8 shows a “true” probability distribution (thick solid line) of D _xx tensor components, three bootstrap estimates (thin solid lines) corresponding to three different original sets, and an estimate obtained from the original set ( A comparison with (vertical line) is shown. The bootstrap estimate of the probability distribution for D _xx is for n = 8 and N _B = 10000. The thick dashed line represents the true distribution and the solid line represents the bootstrap estimate. The vertical dashed line is the original set of estimates used in bootstrap estimation. Since the probability that a bootstrap sample is taken is uniform, the average estimate does not change while the standard error (SE) is a non-parametric maximum likelihood estimate of the true SE. As the number n of images used decreases, the artifacts generated by the bootstrap distribution increase.

FIG. 9A shows data generated using a diffusion phantom. A computer-generated phantom (8 × 1 × 1 voxel) has the following areas: That is, CSF (Trace = 10.0 × 10 ⁻³ mm ² / sec, isotropic), gray matter-GM (Trace = 2.1 × 10 ⁻³ mm ² / sec, anisotropy), maximum When the ratio between the eigenvalue (main diffusivity) and the intermediate eigenvalue is r ₁ , the ratio between the intermediate eigenvalue and the minimum eigenvalue is r _2, and expressed as a pair of (r ₁ , r ₂ ) coordinates, A1 (8,1 ), A2 (4, 1), A3 (2, 1), A4 (1, 4), A5 (1, 2), A6 (3/2, 3/2) and several anisotropic regions It is. Bootstrap samples are obtained for three eigenvectors and the calculated angle (32) for the uncertainty cone for each of the three eigenvectors.

  FIG. 9B shows an image that is the reciprocal of the angle for the minimal cone of uncertainty for the three eigenvectors obtained from the bootstrap method. As can be seen from FIG. 9B, the intensity of each voxel is inversely proportional to the minimum value of the three cone angles.

  By comparing FIG. 9B and FIG. 9A, it can be seen that there is a strong relationship with the known anisotropy of the diffusion tensor in a given voxel. The results obtained from the simulation were validated using data from the living brain. This result shows similar behavior, provided that there are no systematic artifacts. This bootstrap method can facilitate the use of statistical techniques for designing and analyzing DT-MRI. Subject to the use of a sufficient number of images in the bootstrap resampling method, the estimation of uncertainty and the probability distribution of the measured and calculated variables during DT-MRI can be calculated using bootstrap analysis. Obtainable.

(5. Quantitative statistical tests to assess changes in diffusion tensor traces: clinical and biological implications)
We present a general statistical framework for biologically or clinically distinguishing significant changes in the diffusion tensor trace, Trace (D), from background noise.

(5.1 Overview)
Trace (D) is uniform in normal brain parenchyma since the first measurement of Trace (D) (1) and the first demonstration of trace MR images (44), with D as an effective water diffusion tensor. It has been widely reported that it substantially drops in the ischemic region during acute stroke and increases markedly in chronic stroke. Nevertheless, it is uncertain to distinguish from changes in Trace (D) caused by changes in the physiological state of the tissue, its physical properties, or its microstructure.

(5.2 Method)
In the previous section, we showed that the elements of the diffusion tensor obtained by DT-MRI (44) are distributed according to the multivariate Gaussian probability density function in the ROI with spatially uniform diffusion characteristics. This result means that Trace (D) is distributed according to the univariate Gaussian distribution within the same uniform ROI.

However, <Trace (D)> is an average, and σ _T ² is a variance. Furthermore, σ _T includes contributions from D _xx , D _yy , and D _zz (eg, Var (D _xx )) and their covariance (eg, Cov (D _xx , D _yy )).

  In this distribution, the hypothesis can be first formulated with respect to the moment of Trace (D) in the ROI and tested quantitatively using the present invention (see eg (51)). Specifically, whether or not Trace (D) is uniform in normal brain parenchyma, whether or not Trace (D) is significantly reduced in the ischemic region, or Trace (D) is a disease region of brain parenchyma Related hypotheses, such as whether or not to increase, can be tested clinically or biologically. To assess the degree of non-uniformity of Trace (D) at different ROIs, the hypothesis of the distribution of traces at different ROIs can be tested. Prior to the present invention, distribution of traces was never considered, but now using the present invention, distribution of traces can provide valuable physiological information. For example, the variance of Trace (D) can be verified using an F-test adapted for this purpose. Finally, one can use the Kolmogorov-Smirnov test or one of its variants to assess whether Trace (D) is normally distributed within the ROI. This test indicates whether the trace data has been corrupted by systematic artifacts (eg movement).

(5.3 Results and discussion)
A Monte Carlo simulation of a DT-MRI experiment was performed in an ROI containing a diffusion tensor with diffusion properties corresponding to normal or ischemic gray matter (41). Simulations were also performed with different signal-to-noise ratios (SNR). In the simulation using the six four sets of DWI which is obtained by the diffusion gradient oriented isotropically along six different directions, Trace (b) is in the range from 0 to 900 sec / mm ^2.

  FIG. 10 shows selection of individual voxels as regions of interest. Shows that voxels containing gray matter (GM), white matter (WM), and CSF are selected. Each region of interest has a single voxel.

  Using the bootstrap method, an empirical statistical distribution for Trace (D) was determined for the three voxels selected in FIG. 10 based on the diffusion tensor determined for the voxels. In addition, a parametric statistical distribution for Trace (D) was determined for each voxel using a univariate Gaussian distribution. 11A-11C show a comparison of the empirical statistical distribution for Trace (D) and the parametric statistical distribution for Trace (D). Specifically, FIG. 11A shows empirical bootstrap data obtained from the single voxel of FIG. 10 containing gray matter, and the data of FIG. 11A was fitted using a Gaussian distribution. FIG. 11B shows empirical bootstrap data obtained from the single voxel of FIG. 10 containing white matter, and the data of FIG. 11B was also fitted using a Gaussian distribution. FIG. 11C shows empirical bootstrap data obtained from the single voxel of FIG. 10 with CSF, and the data of FIG. 11C was also fitted using a Gaussian distribution. As can be seen from FIGS. 11A-11C, the empirical statistical distribution for Trace (D) closely follows the parametric statistical distribution for Trace (D), and it can be assumed that there are few artifacts in the diffusion weighted image.

By generating many replicates of DT-MRI experiments from a single study using non-parametric methods, or pooling data from a single study to build a distribution of D within the ROI Quantitative hypothesis tests can be constructed for the difference or change in Trace (D) between individual voxels. Therefore, useful features can be determined for Trace (D) in a single voxel within and between different ROIs. As an example, a quantitative hypothesis test for Trace (D) can be constructed as follows.
• Is Trace (D) uniform within the ROI?
Is Trace (D) uniform in normal brain parenchyma?
Is the difference in Trace (D) significant in the two ROIs including brain parenchyma?
• Does Trace (D) drop significantly in ischemic ROI?
• Does Trace (D) increase in disease areas?
• What is the minimum drop in Trace (D) that can be reliably detected at each SNR?
Is the variance of Trace the same for different ROIs to assess the non-uniformity of Trace (D) at different ROIs?

FIG. 12 shows a hypothesis as to whether the difference in ROI average trace measurements is statistically significant at a fixed statistical power. Using an analytic formula that implicitly relates the minimum detectable significant difference δ of Trace (D) to the power of the test, p-level, variance of SNR, and the number of voxels including ROI, 50 voxels And plot δ against SNR for ROI with a statistical power of 0.95. The different curves in FIG. 12 correspond to different p levels, and δ at each SNR increases as the desired confidence level increases. The left axis of FIG. 12 displays the smallest detectable change in Trace (D) (μm ² / sec). Again, the approximately hyperbolic relationship between approximately δ and SNR indicates a trade-off between δ and SNR. Similar results are obtained for the smallest detectable significant difference in the variance of Trace (D).

  Many statistics in MRI, and in particular DT-MRI, are both biased and non-Gaussian. Examples include D sorted eigenvalues (40), their corresponding eigenvectors (64), and diffusion anisotropy measurements (40). Notably, Trace (D) is not biased for SNR greater than about 5 (62), where it is shown to be Gaussian distributed. These two facts make Trace (D) a very powerful parameter.

  This new method of the present invention significantly improves the quality, clinical value, and biological utility of DT-MRI trace data. This is because the statistical analysis of the present invention can now be repeated for any DWI acquisition. The present invention provides Trace (D) and a first quantitative technique for testing hypotheses regarding changes in health, growth, degradation, and disease. Initially, rather than using specialized statistical methods, trace MR imaging experiments can be designed, interpreted, and analyzed using rigorous statistical tests (including detection of statistical artifacts). A confidence interval can be assigned to observe the change in Trace (D). This approach can find applications in long-term multi-site drug discovery and therapeutic efficacy studies, as well as in the diagnosis of, for example, assessment of stroke, tumors, and other diseases and conditions.

  In addition, the present invention can be used to improve the ability to detect minute changes in diffusion properties, such as required when grading tumors or identifying ischemic penumbra. Furthermore, the present invention can be used to detect systematic artifacts (eg, motion) in the DWI for each voxel. Finally, this statistical method can also be applied to segmenting tissue by its diffusion characteristics. This framework can also be extended to handle the validity of other DT-MRI “stains”.

(6. Quantitative test for the variability of the apparent diffusion tensor trace of water: clinical and biological implications)
In the previous section, the effective diffusion tensor trace Trace (D) measured using DT-MRI was described by a data univariate Gaussian distribution whose mean and variance can be estimated directly from DT-MRI data. Quantitative statistical hypothesis testing is the difference between the biologically meaningful changes in Trace (D) (eg changes that occur in health, growth, deterioration, and disease) and the MR background noise present in all diffusion weighted images. Can be designed to identify. Such an assay is whether or not Trace (D) is uniform in normal brain parenchyma for any particular signal-to-noise ratio (SNR), the smallest measurable change in Trace (D). Determining whether there is a significant difference in Trace (D) between the brain region and another brain region. Both long-term and multi-site studies can assess statistically significant differences in Trace (D) data between different tissue regions. In the present invention, the significance of the difference in the variance of Trace (D) can be measured between different voxels, different ROIs, and different subjects. A non-parametric (eg bootstrap) method can be used to determine the second or higher moment of distribution of Trace (D) within each voxel. Deviations from the normality of the distribution of Trace (D) can be used as a sensitive measure of systematic artifacts caused, for example, by object motion in diffusion weighted image (DWI) acquisition. Finally, knowing the distribution of Trace (D) allows the use of statistical-based image segmentation schemes such as k-means to distinguish between different tissue sections based on their diffusion characteristics.

(6.1 Overview)
Following the evolution of DT-MRI (44), one of the DT-MRI imaging parameters, diffusion tensor trace Trace (D), cat (53), dog, macaque (40), and It has been reported that it is spatially uniform within the normal living brain parenchyma of humans (54), (41) and, notably, has approximately the same value in these species (55). These results are surprising when considering the great anatomical and histological differences between gray and white matter and the significant differences in brain structure between these different species. However, if confirmed, these results may have important consequences in comparative physiology, and may have important consequences in early screening and diagnosis of the disease, as described below. There is.

  Next we will address questions about whether these findings are qualitative. First, Trace (D) MRI-based measurements are always subject to background noise (40), and as a result, even for homogeneous media, Trace (D) measurements have inherent variability for each voxel. Show. Therefore, in order to quantitatively test the assertion of uniformity of Trace (D), the statistical hypothesis that the value of Trace (D) in all voxels in normal parenchyma results from the same statistical distribution We must change this proposition. This section deals with the correct form of this distribution, specifically how hypotheses are written and tested using DT-MRI data.

  In acute stroke, it has been reported that the decrease in Trace (D) in the ischemic region is 50% (54). In chronic stroke, the increase can be comparable (54). In many other clinical conditions, the accompanying changes in tissue microstructure, architecture, or physical characteristics may be small. For example, under certain conditions, it may be difficult to distinguish changes in Trace (D) from signal variations due to background radio frequency (RF) noise. Examples include identifying and grading tumors (55), measuring small differences in mean diffusivity between white and gray matter in acute stroke (56), identifying MS lesions (57) , (58), and Perezus-Merzbacher's disease (36), Waller's degeneration (25), and following diffusion changes in neurodegenerative disorders such as Parkinson's disease and Alzheimer's disease (59). If the spatial uniformity of Trace (D) in the normal brain can be quantitatively established, a significant deviation from Trace (D) is a useful and sensitive clinical marker for abnormalities or disease. And can be a prior method for its early detection or screening.

  After the minimal clinically significant increase or decrease level of Trace (D) is established, the new statistical test framework can be used in reverse to optimize (eg, require the least DWI, minimize time) MRI scanning protocol can be designed.

  More generally, despite the usefulness of Trace (D) in clinical diagnosis, different voxels or attention for the same subject during a single scan (eg, to compare normal and abnormal tissues) Compare the value of Trace (D) in the region of interest (ROI), compare the value of Trace (D) in the same ROI of the same subject scanned at different time points (eg, in a long-term study), or ( There is currently no quantitatively exact method available to compare Trace (D) values between ROIs in different subjects (in a multicentric study). At present, only dedicated statistical tests are used for this purpose. This is because the distribution of Trace (D) within each voxel is unknown and therefore parametric-based statistical tests on Trace (D) could not be applied in a meaningful way.

  Finally, Diffusion Weighted Images (DWI) can be contaminated by systematic artifacts such as subject motion, eddy currents, susceptibility differences, etc. (60). At present, there are not enough schemes to test and assess the severity of such artifacts in DWI. This section further provides a prescription for detecting phylogenetic artifacts in each voxel of DWI by evaluating the deviation of that distribution from the known distribution of Trace (D).

(6.2 Method)
In the previous section, we showed that the elements of the diffusion tensor obtained by DT-MRI are distributed according to the multivariate Gaussian probability density function within the ROI with spatially uniform diffusion characteristics. D is a 6-dimensional vector

This distribution can be written as:

_Where M = (μ _xx , μ _yy , μ _zz , μ _xy , μ _xz , μ _yz ) ^T is a 6-dimensional average vector, and Σ may be negative for off-diagonal elements 6 × 6 covariance matrix.

  In the theory of multivariate statistical analysis,

It is well known that any linear combination of multivariate Gaussian distribution variables such as must be distributed according to a univariate Gaussian distribution (51).

One linear combination of

Trace (D) = (1,1,1,0,0,0) (D xx, D yy, D zz, D xy, D xz, D yz) T = D xx + D yy + D zz = 3 <D> (5)

  In the above formula, <D> is a rotationally invariant average diffusion rate (or average ADC) averaged in a direction. Then, within a particular voxel or homogeneous ROI, Trace (D) is distributed according to:

Where μ is the population mean and σ _T ² is the population variance. Where

μ = (1, 1, 1, 0, 0, 0) (μ _xx , μ _yy , μ _zz , μ _xy , μ _xz , μ _yz ) ^T = μ _xx + μ _yy + μ _zz (7)

  And,

σ _T ² = (1,1,1,0,0,0) Σ (1,1,1,0,0,0) ^T = σ ² _xxxx + σ ² _yyyy + σ ² _zzzz + _2σ ² _xxyy + σ ² _yyzz + σ ² _xxzz (8)

  Where

σ ² _xxxx = Var (D _xx ), σ ² _yyyy = Var (D _yy ), σ ² _zzzz = Var (D _zz ) (9)

  And,

σ ² _xxyy = Cov (D _xx , D _yy ), σ ² _yyzz = Cov (D _yy , D _zz ), σ ² _xxzz = Cov (D _xx , D _zz ) (10)

It can be seen that the population average of Trace (D) is the sum of the population average of the three diagonal elements of D. However, the population variance of Trace (D) is the variance of the diagonal elements of the diffusion tensors D _xx , D _yy , D _zz (eg, Var (D _xx )) and its covariance (eg, Cov (D _xx , D _yy). )). In general, it is all distributed positive, covariance may take either sign, the total variance sigma _T ² of Trace (D), can contribute to either positive or negative. Furthermore, there is no a priori reason for the disappearance of these covariance terms, and early experiments with phantoms have shown that these terms are generally not zero (17).

In general, the population values are μ, σ _T ² and Σ is unknown a priori. Therefore, population values must be estimated from experimental data. This can be done in two ways. First, D is estimated for each voxel using multivariate linear regression over the complete set of DWIs, and from this D sample estimates of μ, σ _T ² , and Σ (17), or these estimates are obtained. Second, using a bootstrap method that iteratively samples a subset of the original data with permutations as described in the previous section, D is estimated for each voxel, and a diffusion tensor element such as Trace (D) and its Determine the moment of the function empirically.

  Since the distribution of Trace (D) is well known, the present invention can formulate and quantitatively test the hypothesis for that moment in an individual voxel or ROI with respect to the first time (eg, (51 )). Specifically, clinical or biology, such as whether Trace (D) is uniform in normal brain parenchyma or whether Trace (D) is lowered or elevated in diseased areas of brain parenchyma. Relevant hypotheses can be tested.

  There are several tests that can be applied to establish whether Trace (D) is uniform within the ROI. For example, the following test can be performed. Whether the distribution of Trace (D) is described by a distribution with a single average for a given level of background noise. Whether the distribution of Trace (D) is described by a distribution with a single variance for a given level of background noise. Whether the distribution of Trace (D) is described by a normal distribution for a given level of background noise. A t-test is used to test the single-mean null hypothesis of Trace (D). The F test is used to test the single variance null hypothesis of Trace (D). The Kolmogorov-Smirnov test is used to test the normal distribution of Trace (D).

  In order to evaluate the difference in Trace (D) between two different ROIs, the hypothesis of whether the trace means are different and whether the variance of the traces is different between the two ROIs can be tested. If either is different, it can be concluded that there is a significant difference between them. Prior to the present invention, the distribution of traces was never examined, but the distribution of traces now provides useful physiological information using the present invention.

  Finally, the Kolmogorov-Smirnov test or the Kuiper test (52) can be used to assess whether Trace (D) is normally distributed within the ROI. From the basic principle, it is well known that Trace (D) is normally distributed within each voxel in the absence of systematic artifacts (eg due to patient movement), so Trace (D) is normally distributed within each voxel. If not, it is destroyed by systematic artifacts. For example, FIG. 13 shows detection of artifacts in a diffusion weighted image. In FIG. 13, the distribution of Trace (D) obtained through the bootstrap method is not described by a Gaussian probability density function.

  The Trace (D) test can be pre-formed for each voxel. This assay is accomplished using a bootstrap method. The bootstrap method is a resampling technique, where an empirical distribution of diffusion tensor values is obtained for each voxel from a single set of diffusion weighted images. This method and its application to DT-MRI was described in the previous section.

  If it is desirable not to do a priori assignment of tissue within a particular ROI, and it is desirable to segment such tissue regions based on the value of Trace (D), Trace (D) will be uniform. An interactive scheme can be used to determine certain regions (ie, Trace (D) matches that taken from a Gaussian distribution with the same mean and variance).

As discussed above, Trace (D) and other quantities are preferably determined based on the determination of the diffusion tensor from seven or more diffusion weighted images. Optionally, these quantities such as Trace (D) can be approximated, for example using fewer 5, 4, 2 or 1 diffusion weighted images. Several methods have recently been reported to obtain an estimate of Trace (D) without directly calculating the total diffusion tensor. For example, an estimate of Trace (D) can be obtained by taking the sum of four tetrahedrally encoded diffusion weighted images, where each image is normalized by a non-diffusion weighted image. This approach was proposed in (63) and (64). An estimate of Trace (D) can also be obtained by taking the sum of three apparent diffusion coefficients obtained from three diffusion weighted images whose diffusion gradients are applied along three orthogonal directions. An example of this technique is given in (53). In either case, if all the cross terms cannot be removed in the diffusion weighted imaging sequence, these quantities are only approximations to Trace (D) and each of the diffusion weighted images is Have the same Trace ( b ) value. Other schemes have been proposed to obtain “anisotropic weighted” or trace weighted images with even less diffusion weighted images. In fact, some groups have proposed using only two diffusion weighted images to obtain an estimate of Trace (D). This is done by acquiring one diffusion weighted image that is not diffusion weighted and another diffusion weighted image with an “anisotropic” weight. Examples of this approach are given in (65), (66), and (67). At present, statistical distributions using any of the methods proposed above, bias in means and variances, and other features of these Trace (D) estimates have not yet been investigated.

(6.3 Results and Discussion)
A phantom study was undertaken to determine empirically whether Trace (D) is a Gaussian distribution in a homogeneous isotropic phantom. In this case, a water phantom containing 0.5% polyacrylic acid (500,000 MW) per volume is used. Long chain polymers present in such low concentrations do not affect the water diffusivity of the bulk solution, and the diffusion of water such as mechanical vibrations (shear mode and bulk mode) and convection due to thermal gradients occurring in the phantom. Suppress some potential empirical artifacts that can be mistaken. A thermal blanket was also used to ensure temperature uniformity within 0.1 ° C. throughout the phantom. This further reduces the possibility of Rayleigh convection occurring in this sample, limiting thermal fluctuations in the diffusion coefficient in the sample to approximately 1.5% per degree Celsius (61).

  This MRI system was pre-calibrated (18) using a method similar to that outlined above to ensure that it is applied when obtaining the correct slope factor DWI. Other well-established techniques were used to reduce other artifacts such as eddy current effects (see (21)). Magnetic susceptibility artifacts are only present near the container wall, so the region of interest is always chosen far away from it. The b matrix for each DWI acquisition is numerically calculated using software and a computer (13), (12), (3). Using the method outlined in (17), the diffusion tensor is estimated using multivariate linear regression using the measured intensity of the DWI and its corresponding calculated b matrix.

  The described embodiments and the examples discussed herein are non-limiting examples.

  Although the invention has been described in detail with reference to preferred embodiments, it will be apparent to those skilled in the art from the foregoing that changes and modifications can be made without departing from the invention in its broader aspects. Accordingly, the invention as defined in the claims is intended to cover all such changes and modifications as fall within the true spirit of the invention.

Embodiments of the present invention will be described in more detail with reference to the drawings. Here, the same reference numbers refer to the same features.
It is a flowchart for analyzing a DT-MR signal. Figure 5 is a flow diagram for analyzing DT-MR signals for at least two regions of interest. It is a flowchart for analyzing the DT-MR signal for the first time point and the second time point. It is a flowchart for analyzing a DT-MR signal, without determining a diffusion tensor. It is a figure which shows the probability distribution of six independent components of the effective diffusion tensor obtained from a Monte Carlo simulation. It is a figure which shows the probability distribution of the trace in the area | region to watch (ROI). It is a figure which shows the probability distribution obtained within a single voxel. FIG. 6 shows a comparison between a “true” probability distribution tensor component and an estimate obtained from the original set. It is a figure which shows the data produced | generated using a diffusion phantom. FIG. 6 shows an image that is the reciprocal of the angle for a minimal cone of uncertainty for three eigenvectors obtained from the bootstrap method. It is a figure which shows selecting each voxel. FIG. 11 shows empirical bootstrap data obtained from the single voxel of FIG. 10 containing gray matter. FIG. 11 shows empirical bootstrap data obtained from the single voxel of FIG. 10 including white matter. FIG. 11 illustrates empirical bootstrap data obtained from the single voxel of FIG. 10 including CSF. FIG. 5 shows a hypothesis test of whether a difference in ROI mean trace measurements is statistically significant at a fixed statistical power. It is a figure which shows the detection of the artifact in a diffusion weighted image.

Claims (9)

A computer-readable medium having readable stored software for causing a computer system to execute a procedure for analyzing a diffusion tensor magnetic resonance signal, the procedure comprising:
Obtaining at least one diffusion-weighted signal, each of the diffusion-weighted signals having a first sampling step having a plurality of voxels;
A second sampling step of obtaining each resampled diffusion enhanced signal by sampling each of the diffusion enhanced signals;
Approximating from the resampled diffusion weighted signal a quantity related to the diffusion tensor per voxel based on a statistical estimate of the diffusion tensor;
Determining an empirical statistical distribution for the amount associated with the diffusion tensor from the amount associated with the diffusion tensor;
A computer-readable medium comprising:   The computer-readable medium of claim 1, wherein the quantity associated with the diffusion tensor is an approximation of a trace of the diffusion tensor.   The computer-readable medium of claim 1, wherein the function of the diffusion tensor is any one of a main diffusivity, a rotation invariant measure, a relative anisotropy, a diffusion tensor deviation, and an eigenvector.   The computer-readable medium of claim 1, further comprising investigating an object based on features of an empirical statistical distribution for the quantity.   The computer-readable medium of claim 1, wherein the statistical estimation includes multivariate regression. An apparatus for analyzing a diffusion tensor magnetic resonance signal,
Means for obtaining at least one diffusion-weighted signal, each of the diffusion-weighted signals having first sampling means having a plurality of voxels;
Second sampling means for obtaining each resampled diffusion enhanced signal by sampling each of the diffusion enhanced signals;
Means for approximating a quantity associated with a per-voxel diffusion tensor based on a statistical estimate of the diffusion tensor from the resampled diffusion weighted signal;
Means for determining an empirical statistical distribution for the amount associated with the diffusion tensor from the amount associated with the diffusion tensor;
A device comprising:   The computer-readable medium of claim 1, further comprising identifying a fiber path of an object based on characteristics of an empirical statistical distribution for the quantity.   The computer-readable medium of claim 1, wherein the amount associated with the diffusion tensor is approximated without determining the diffusion tensor.   The computer-readable medium of claim 1, wherein the diffusion weighted signal represents diffusion weighting, and an amount associated with the diffusion tensor is approximated by less than seven diffusion weighted images.

Images