A Linear Systems Description of Multi-Compartment Pulmonary ~(129)Xe Magnetic Resonance Imaging Methods

摘要

Objective: We aimed to develop a linear-systems model to evaluate the impact of mathematical assumptions related to multi-compartment ~(129)Xe MRI methods. We employed a linear-systems approach to fill a knowledge gap associated with a single-point Dixon approach currently used for magnetization calculations and physiologic estimates. Methods: We generated a linear-systems model for magnetization calculations needed to generate multi-compartment ~(129)Xe MRI data. ~1Lung tissue and red-blood-cell compartments were isolated by acquiring data 90° out of phase and aligned with perpendicular quadrature channels. Results: In our linear-systems model, a single-lobe sine-pulse in the time domain was used to excite ~(129)Xe atoms in the tissue and red blood-cell compartments. We assumed that T2* exponential decay in the time domain was equivalent to convolution with a complex Lorentzian function in the frequency domain, and the gradient echo envelope was equivalent to convolution with a rectangular pulse with phase shifting. A rectangular window function and Dirac comb sampling in the time domain modeled analog-to-digital recording. Fast Fourier transforms were modelled by Dirac combs in both time and frequency domains. To account for non-uniform sampling, k-space was re-sampled using a unique sampling function convolution followed by Cartesian sampling. Phase inhomogeneities were corrected using reference gas and spectroscopy data. Conclusion: The proposed linear-system analysis provides a framework for modelling decay constants, peak overlap, and magnetization evolution common in multi-compartment ~(129)Xe MRI. Understanding the spectral properties of ~(129)Xe MRI will provide a way to identify novel compartments and their abnormalities in diverse pulmonary diseases.