Analysis of the transient phase of balanced SSFP with non-continuous RF for cardiac imaging

Introduction

The transient phase of balanced SSFP (bSSFP) is the period during which magnetization approaches steady state. The transient phase of non-ECG-gated, continuous-RF bSSFP has been characterized by a simple exponential decay with a time constant that is a flip-angle-weighted average of T₁ and T₂ [1]. Cardiac imaging applications, however, often utilize bSSFP with non-continuous RF excitation. The example considered here, Look-Locker-based T₁ mapping, begins with an ECG trigger, and is followed by magnetization preparation, a bSSFP imaging segment, and a recovery time prior to the subsequent ECG trigger. Multiple time points are acquired, separated by the R-R interval T_RR. The description of the continuous-RF transient phase is not applicable in this case.

Purpose

The goal of this work was to develop an analytical expression for the transient phase of bSSFP with non-continuous RF excitation. The resulting equation can be applied to Look-Locker acquisitions to provide true quantification of T₁ (and T₂), rather than an "apparent" T₁ (T₁*).

Methods

The pulse sequence is shown in Figure 1 and is periodic, beginning with data acquisition (a segment of N views) and ending with a recovery time T_rec = T_RR-N × TR before the next segment. Let M_T(n) be the transient magnetization prior to time point n, and assume the magnetization at the subsequent time point is reduced to λM_T(n) [1, 2]. The transient response may then be written

This work will show that

where R_{x, z} are rotation matrices for RF excitation/alternation, E _t represents relaxation during time t, and B denotes steady-state catalyzation. The equation AM_T(n) = λM_T(n) can be solved for the real eigenvalue λ _eig (T₁, T₂) of A, which is a function of T₁, T₂, and known imaging parameters. Because it describes the exponential evolution of the transient magnetization, λ can also be written

T₁* can be determined from fitting the time point images acquired during the transient phase. With an appropriate pulse sequence, λ _eig (T₁, T₂) = λ _image can be solved for T₁ and T₂.

Figure 1

Pulse sequence diagram, M _T ( n) is the transient magnetization prior to data acquisition at time point n.

Results

Bloch simulation of the pulse sequence in Figure 1 was performed, and T₁* was determined by curve fitting. T₁, T₂, and T₁* were then calculated using λ _eig (T₁, T₂) and showed perfect agreement.

Conclusion

Previously reported cardiac T₁ mapping techniques using bSSFP have employed various assumptions and approximations to estimate T₁. This work presents an analytical expression for the transient phase of non-continuous-RF bSSFP. It provides the ability to directly quantify T₁&T₂ for cardiac imaging while obviating such assumptions in acquisition or post-processing.