Exploiting Geometric Constraints for Parameter Quantification in Balanced Steady-State Free Precession MRI

Abstract

Balanced Steady-State Free Precession (bSSFP) is a magnetic resonance imaging (MRI) sequence well known for its high signal-to-noise ratio efficiency and T2/T1 contrast that suffers from banding artifacts caused by its dependence on static magnetic field inhomogeneities. While phase-cycling is a common remedy to banding, the complex, biphasic nature of the bSSFP signal has historically made its rich phase information difficult to exploit for quantitative tissue and field mapping. This work overcomes this challenge by introducing novel techniques for parameter quantification in bSSFP MRI, and exploiting the geometric constraints of its unique signal profile, which forms a parameterized ellipse in the complex plane. First, a parameter quantification method using four phase-cycled bSSFP acquisitions is established via the geometric property of the signal ellipse's cross-point. An auxiliary circle with a one-to-one correspondence to the bSSFP signal ellipse is considered, facilitating the elucidation of ESM parameters and leading to an analytic ''ellipse unlocking'' method. This cross-point formalism allows for the direct extraction of ellipse parameters, from which quantitative maps of the transverse relaxation time T2 and field-related phase components are generated. Building on the identified information redundancy within the signal ellipse, the second project develops an analytical solution requiring only three phase-cycled acquisitions, further exploiting the inherent constraints. This Direct Analytic Solution (DAS) is derived from a linear system during the ellipse-to-circle transformation, formally reducing the data redundancy. However, analysis reveals that DAS is highly noise- and banding-sensitive and fails in specific scenarios. This investigation indicates the limitations of a purely analytical approach with minimal data, thereby motivating the search for a more robust method. To overcome these limitations, a robust numerical method was developed using three acquisitions. This approach imposes a new geometric constraint—that the signal ellipse passes through the origin—to create a simplified model. A regularized joint optimization procedure then solves the resulting nonlinear least-squares problem, yielding artifact-free images and quantitative B0 maps. A practical challenge common to all these quantification methods is the effective, phase-preserving combination of solutions from multi-channel coil data. An accurate, phase-preserving solution combination strategy is therefore critical for robust quantification performance. The Optimal Weighted Average (OWA) method is implemented for this purpose, which uses regional variance weighting to combine these solutions effectively. The optimality of the weighting scheme is confirmed through mathematical derivation, and efficacy in reducing noise is demonstrated with experiments. Collectively, this thesis demonstrates how geometric constraints can be leveraged for robust and highly efficient parameter quantification from phase-cycled bSSFP MRI, achieving accurate results with a minimal number of acquisitions.