4.7 Article

Accuracy of the Morphology Enabled Dipole Inversion (MEDI) Algorithm for Quantitative Susceptibility Mapping in MRI

Journal

IEEE TRANSACTIONS ON MEDICAL IMAGING
Volume 31, Issue 3, Pages 816-824

Publisher

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TMI.2011.2182523

Keywords

Error analysis; magnetic resonance imaging (MRI); morphology enabled dipoleinversion (MEDI); quantitative susceptibility mapping

Funding

  1. National Institutes of Health (NIH) [R01 NS072370, R01 EB013443]

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Determining the susceptibility distribution from the magnetic field measured in a magnetic resonance (MR) scanner is an ill-posed inverse problem, because of the presence of zeroes in the convolution kernel in the forward problem. An algorithm called morphology enabled dipole inversion (MEDI), which incorporates spatial prior information, has been proposed to generate a quantitative susceptibility map (QSM). The accuracy of QSM can be validated experimentally. However, there is not yet a rigorous mathematical demonstration of accuracy for a general regularized approach or for MEDI specifically. The error in the susceptibility map reconstructed by MEDI is expressed in terms of the acquisition noise and the error in the spatial prior information. A detailed analysis demonstrates that the error in the susceptibility map reconstructed by MEDI is bounded by a linear function of these two error sources. Numerical analysis confirms that the error of the susceptibility map reconstructed by MEDI is on the same order of the noise in the original MRI data, and comprehensive edge detection will lead to reduced model error in MEDI. Additional phantom validation and human brain imaging demonstrated the practicality of the MEDI method.

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