Radiotekhnika
Publishing house Radiotekhnika

"Publishing house Radiotekhnika":
scientific and technical literature.
Books and journals of publishing houses: IPRZHR, RS-PRESS, SCIENCE-PRESS


Тел.: +7 (495) 625-9241

 

Measurement of magnetic gradients in MRI. Part 1. The model and algorithms

DOI 10.18127/j15604128-201701-06

Keywords:

A.V. Protopopov – Post-graduate Student, Moscow Institute of Physics and Technology (State University), FSCC after the name of Dmitri Rogachev E-mail: proto.alex@hotmail.com


The technique of a gradient recalled echo (GRE) became a powerful tool for sensing tiniest heterogeneities of magnetic field inside a human body. GRE sequences are used to depict hemorrhage, calcification, iron deposition in various tissues and lesions, to measure capillary dimensions and densities, for characterization of bone structure, mapping of brain iron content, and are the basis of the blood oxygen level dependent (BOLD) technique. Traditionally, in GRE magnetic resonance imaging (MRI), the image is formed by variations of an echo signal, which may be considered as some type of rendering but not as a map of a certain measured parameter. Such a rendering, whatever helpful it is for visual perception, does not answer the question what exactly physical parameter we see. Therefore, in GRE MRI, an important problem is identification of physical parameters that make an echo signal, and mapping them in a form of an image. The GRE signal evolves as a combined result of irreversible transverse relaxation processes T2, determined by spin-spin interactions on a quantum-mechanical level, and heterogeneities in the static magnetic field described by classical electrodynamics. Once separated, T2 and background gradients are two clear physical parameters that may be used for creating independent GRE images, thus providing additional information for diagnostics. Commonly used techniques for separating contribution of T2 relaxation from contribution by background gradients are based on one-dimensional models and fitting known decay functions into experimental relaxation curves. Namely, the T2 relaxation is always assumed to be monoexponential and contribution of the background gradient is represented by sinc function. However, in the one-dimensional model, the sinc function oscillates, which happens in reality only on rare occasions of newly installed scanners with uncompensated coils. In all other practical cases the experimental relaxation curves do not show oscillations. To cope with this artificial problem, the fitting procedures are usually limited to the first zero of sinc function, thus preserving only positive values. This results in ignoring information from longer echo intervals, making the measurement inaccurate. There are also other drawbacks of the fitting algorithms. In the present publication, we introduce: the three-dimensional relaxation model consistent with experiments; fittingless algorithms for separating T2 relaxation from background gradients.

References:

 

  1. Tang M.E., Chen T.W., Zhang X.M., Huang X.H. GRE T2*-Weighted MRI. Principles and Clinical Applications // BioMed Research International. 2014. Article ID 312142. URL = http://dx.doi.org/10.1155/2014/312142.
  2. Chavhan G.B., Babyn P.S., Manohar B.T., Shroff M., Haacke E.M. Principles, Techniques, and Applications of T2*-based MR Imaging and Its Special Applications // RadioGraphics. 2009. 29. P. 1433−1449.
  3. Bloch F. Nuclear induction // Phys. Rev. 1946. V. 70. № 7−8. P. 460−474.
  4. Torey H.C. Bloch Equations with Diffusion Terms // Phys. Rev. 1956. V. 104. № 3. P. 563−565.
  5. Yablonskiy D.A., Haacke E.M. Theory of NMR signal behavior in magnetically inhomogeneous tissues – the static dephasing regime // Magn Reson Med. 1994. V. 32. № 6. P. 749−763.
  6. Sukstanskii A.L., Yablonskiy D.A. Gaussian approximation in the theory of MR signal formation in the presence of structure-specific magnetic field inhomogeneities // Journal of Magnetic Resonance. 2003. V. 163. P. 236−247.
  7. Sukstanskii A.L., Yablonskiy D.A. Gaussian approximation in the theory of MR signal formation in the presence of structure-specific magnetic field inhomogeneities. Effects of impermeable susceptibility inclusions // Journal of Magnetic Resonance 2004. V. 167. P. 56−67.
  8. Kiselev V.G. Effect of magnetic field gradients induced by microvasculature on NMR measurements of molecular self-diffusion in biological tissues // Journal of Magnetic Resonance. 2004. V. 170. P. 228−235.
  9. Dickson J.D., Ash T.W.J., Williams G.B., Sukstanskii A.L., Ansorge R.E., Yablonskiy D.A. Quantitative phenomenological model of the BOLD contrast mechanism // Journal of Magnetic Resonance. 2011. V. 212. P. 17−25.
  10. Knight M.J., Kauppinen R.A. Diffusion-mediated nuclear spin phase decoherence in cylindrically porous materials // Journal of Magnetic Resonance. 2016. V. 269. P. 1−12.
  11. D’Avila M.A., Powell R.L., Phillips R.J., Shapley N.C., Walton J.H., Dungan S.R. Magnetic resonance imaging [MRI]: a technique to study flow and microstructure of concentrated emulsions // Brazilian Journal of Chemical Engineering. 2005. V. 22. №. 1. P. 49−60.
  12. Schad L.R., Brix G., Zuna I., Harle W., Lorenz W.J., Semmler W. Multiexponential proton spin-spin relaxation in MRI of human brain tumors // Journal of Computer assisted Tomography. 1989. V. 13. № 4. P. 577−587.
  13. Hagberg G.E., Indovina I., Sanes J.N., Posse S. Real-time quantification of T2* changes using multiecho planar imaging and numerical methods // Magn Reson Med. 2002. V. 48. P. 877−882.
  14. Fernandez-Seara M.A., Wehrli F.W. Postprocessing technique to correct for background gradients in image-based R2* measurements // Magn Reson Med. 2000. V. 44. P. 358−366.
  15. Dahnke H., Schaeffter T. Limits of detection of SPIO at 3.0T using T2* relaxometry // Magn Reson Med. 2005. V. 53. P. 1202−1206.
  16. Hofstetter L.W., Morrell G., Kaggie J., Kim D., Carlston K., Lee V.S. T2* measurement bias due to concomitant gradient fields // Magnetic Resonance in Medicine. 2016 (accelerated publication).
  17. Yang X., Sammet S., Schmalbrock P., Knopp M.V. Postprocessing correction for distortions in T2* decay caused by quadratic cross-slice B0 inhomogeneity // Magn Reson Med. 2010. V. 63. P. 1258−1268.
  18. Bernstein M.A., Zhou X.J., Polzin J.A., King K.F., Ganin A., Pelc N.J., Glover G.H. Concomitant gradient terms in phase contrast MR: analysis and correction // Magn Reson Med. 1998. V. 39. P. 300−308.
  19. Marquardt D.W. An algorithm for least-squares estimation of nonlinear parameters // Journal of the Society for Industrial and Applied Mathematics. 1963. P. 11. № 2. P. 431−441.

 

© Издательство «РАДИОТЕХНИКА», 2004-2017            Тел.: (495) 625-9241                   Designed by [SWAP]Studio