Understanding the morphological mismatch between magnetic susceptibility source and t2* image.

Abstract

Background and purpose: Recent research has shown that a T2* image (either magnitude or phase) is not identical to the internal spatial distribution of a magnetic susceptibility (χ) source. In this paper, we examine the reasons behind these differences by looking into the insights of T2*-weighted magnetic resonance imaging (T2*MRI) and provide numerical characterizations of the source/image mismatches by numerical simulations.

Methods: For numerical simulations of T2*MRI, we predefine a 3D χ source and calculate the complex-valued T2* image by intravoxel dephasing in presence and absence of diffusion. We propose an empirical α-power model to describe the overall source/image transformation. For a Gaussian-shaped χ source, we numerically characterize the source/image morphological mismatch in terms of spatial correlation and FWHM (full width at half maximum).

Results: In theory, we show that the χ-induced fieldmap is morphologically different from the χ source due to dipole effect, and the T2* magnitude image is related to the fieldmap by a quadratic transformation in the small phase angle regime, which imposes an additional morphological change. The numerical simulations with a Gaussian-shaped χ source show that a T2* magnitude image may suffer an overall source/image morphological shrinkage of 20% to 25% and that the T2* phase image is almost identical to the fieldmap thus maintaining a morphological mismatch from the χ source due to dipole effect.

Conclusion: The morphological mismatch between a bulk χ source and its T2* image is caused by the 3D convolution during tissue magnetization (dipole effect), the nonlinearity of the T2* magnitude and phase calculation, and the spin diffusion effect. In the small phase angle regime, the T2* magnitude exhibits an overall morphological shrinkage, and the T2* phase image suffers a dipole effect but maintains the χ-induced fieldmap morphology.