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


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 TRR. The description of the continuous-RF transient phase is not applicable in this case.


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*).


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 Trec = TRR-N × TR before the next segment. Let MT(n) be the transient magnetization prior to time point n, and assume the magnetization at the subsequent time point is reduced to λMT(n) [1, 2]. The transient response may then be written

This work will show that

where Rx, z are rotation matrices for RF excitation/alternation, E t represents relaxation during time t, and B denotes steady-state catalyzation. The equation AMT(n) = λMT(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
figure 1

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


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.


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.


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  2. Hargreaves : MRM. 2001, 46: 149

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Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Slavin, G.S. Analysis of the transient phase of balanced SSFP with non-continuous RF for cardiac imaging. J Cardiovasc Magn Reson 12 (Suppl 1), P230 (2010).

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