《Handbook of MRI Pulse Sequences》原著：MATT A. BERNSTEIN, KEVIN F. KING, XIAOHONG JOE ZHOU, Balanced SSFP (True FISP) To establish SSFP, the gradient area on any axis must not vary among the TR intervals. If a further condition is imposed that the gradient area on any axis is zero during each TR interval, a very different steady state results. The peaks of the SSFP-FID and SSFP-echo will coalesce; that is, they rephase at the same time TE. Therefore the balanced SSFP signal is the coherent sum of the two signals (Oppelt et al. 1986; Duerk et al. 1998). Equation (14.15) is no longer valid because the analysis used to derive it assumes that the two signals are well separated in time. Also, unlike Eq. (14.15) the magnitude of the signal (and not just its sign as in Figure 14.7b) now depends on whether the RF excitation pulses all have the same phase or are sign alternated. The result with sign alternation is: 平衡稳态自由进动（True FISP） 为了建立稳态自由进动，TR 间期的每个轴上的梯度面积必须一样。如果进一步加强条件，每个 TR 间期各轴的梯度面积为零，那么将得到一个十分不同的稳态结果。SSFP-FID 与 SSFP-echo 信号的峰将合并；也就是说，它们在相同 TE 时刻都将达到聚相。因此平衡稳态自由进动信号是两个信号相干的和（Oppelt et al. 1986; Duerk et al. 1998）。方程 （14.15）将不再适用，因为它成立的条件是假设这两个信号在时间上分得比较开。另外，与方程（14.15）不同，平衡稳态自由进动的信号（不仅仅是图 14.7b 所示的符号差别）依赖于是射频激励脉冲是否拥有相同的相位或相位交替。射频激励脉冲符号交替时：
and without sign alternation:
射频激励脉冲符号相同时：
Note the use of T2 rather than T2* in the exponential in Eqs. (14.23) and (14.24). As shown in Scheffler and Hennig (2003), this is correct if the balanced SSFP signal is rephased in the center of the TR interval (i.e., TE = TR/2), in which case
. As the peak of the balanced SSFP signal is moved away from the center of the TR interval, T2' weighting is introduced. In practice, the amount of T2' weighting is usually negligible because a very short TR is used and also because the homogeneity requirements are stringent in balanced SSFP imaging. But it is interesting to note that contrary to spoiled or SSFP-FID pulse sequences, decreasing TE can increase susceptibility weighting in balanced SSFP.注意到公式（14.23）与（14.24）中的指数部分用的是 T2 而不是 T2*。如 Scheffler and Hennig（2003） 所示，如果平衡稳态自由进动信号在 TR 间期的中间时刻相位重聚时（即 TE = TR/2）这是正确的，那么此时 。当平衡稳态自由进动信号形成时不在 TR 间期的中心，而是偏移了的话，那么就会引入 T2' 加权。在实际应用中，T2' 加权的量通常可以忽略不计，因为所使用的 TR 非常短，而且在平衡稳态自由进动成像时主磁场的均匀性要求是十分严格的。但值得注意的是，与扰相梯度回波和 SSFP-FID 序列相反，降低 TE 在 balanced SSFP 序列中会增加磁敏感加权。
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为什么 decreasing TE can increase susceptibility weighting in balanced SSFP？
下面我们先来作关于 TE, T1, T2 的函数 f(TE,T1,T2) 的曲线，看看它随着 TE 的变化情况。
可以看到，当翻角不变，以给定的 T1、T2 条件下，当 TE 缩短时（TR=2TE），信噪比是增高的，但它是如何表现出磁化率权重的增加的呢？
Balance SSFP 序列对主磁场的均匀性要求较高，如果匀场不好时就会在图像中产生磁化率伪影、黑带伪影：
但还是不能解释为什么 TE 缩短，磁化率权重的增加。我想这里所说的缩短 TE，不是常规意义上的同时缩短 TE 与 TR（且保持 TR=2TE），而是考虑的是 TR 固定，考虑 T2' 对于图像的影响：
从下文的相位与信号强度的关系曲线中能够窥得其成立性，因此，在序列扫描时，尽量调整参数严格使得 TR=2TE，减少 T2' 带来的磁化率伪影。
The signal in Eq. (14.23) is greater than (14.24), so in practice sign alternation is used. Physically, the effect of the sign alternation is analogous to the driven equilibrium methods discussed in Section 17.4. The RF pulses with negative flip angle help to drive the longitudinal magnetization back to its equilibrium position, increasing signal when TR is much less than T1.方程（14.23）比方程（14.24）的信号强度要高，因此在实际应用中通常使用射频极性交替的激发方案。实际上，射频脉冲的正负交替可以跟 17.4 节所讨论的驱动平衡方法进行类比。负相位的脉冲翻转角帮助驱动纵向磁化矢量回到它的平衡位置，这样当 TR 远远小于 T1 时能够增加信号强度。
任何 θ 脉冲都具有 90° 与 180° 的效能，那么 -θ 在这里就具有类似 DRIVE 中的 -90° 脉冲的效能。
The effect of sign alternation is equivalent to a pulse sequence (without sign alternation) that has constant precession of the transverse magnetization by Φ=180° in each TR interval (Hinshaw 1976). Similarly, if a constant precession Φ=180° per TR interval occurs in a sign-alternated pulse sequence, it effectively removes the sign alternation, so that the lower signal represented by Eq. (14.24) results. A spatial region where this signal loss occurs is known as a band. Figure 14.8 shows a representative plot of signal versus Φ with and without sign alternation. As described in Carr (1958), the shape of the curves in the plot depends on T1, T2, and θ. Because unwanted phase shifts are usually present in MRI, banding is a serious problem in balanced-SSFP imaging. Assuming a constant resonance offset, the accumulated phase Φ is proportional to the repetition time. Therefore short TR (e.g., 7 ms or less) is key to eliminating banding artifacts, especially because susceptibility variation is inevitable and can rarely be shimmed out completely. Technological strides in obtaining shorter TR (e.g., more powerful gradients), field homogeneity, and eddy-current compensation have allowed balanced SSFP to become a clinically important pulse sequence. Note that balanced SSFP becomes progressively more difficult to implement as the field strength B0 increases, not only because of increased susceptibility variations (measured in hertz), but also because SAR becomes a concern with the use of very short TR.射频脉冲符号交替产生的效果与射频脉冲符号保持不变时每个 TR 间期内横向磁化矢量进动产生恒定的 Φ=180° 的效果是一样的。同理，如果射频脉冲符号的交替的 Balanced SSFP 序列的每个 TR 间期内横向磁化矢量进动产生恒定的 Φ=180° 相位，那么等效于射频脉冲符号保持不变所产生的效果，因此方程（14.24）的信号强度更低。图像上一空间区域的信号丢失称之为黑带伪影。图 14.8 显示了一具有代表性的使用与不使用符号交替射频脉冲所产生的信号强度与相位 Φ 的关系图表。如 Carr （1958）中所述，图表中曲线的形状依赖于所选择的 T1，T2 与 θ 值。由于在磁共振成像中通常总会有不希望产生的相位偏移，因此黑带伪影在平衡稳态自由成像中是一个严重的问题。假设一固定的偏共振频率，那么累积的相位 Φ 与重复时间成正比。因此在平衡稳态自由运动序列中使用短 TR（例如 7ms 或更短）对于消除黑带伪影很重要，尤其是当磁化率变化不可避免以及匀场不能完全匀好时。技术的进步能够获得更短的 TR（即更强的梯度性能）、更好的主磁场均匀性以及涡电流补偿，使得平衡稳态自由进动序列成为临床一个重要的脉冲序列。另外需要注意的是，平衡稳态自由进动序列随着 B0 场的升高也越来越难以扫描，不仅因为磁化率差异的增加（以 Hz 为单位），而且还有 SAR 值也成为一个需要关心的问题，因为使用的 TR 非常短。
For short TR (i.e., TR ≪ T2 < T1 ), the signal formulas can be simplified because E1 ≈ 1 - TR/T1, and E2 ≈ 1 - TR/T2. In that case the signal from sign-alternated balanced SSFP can be expressed as a function of T1/T2:对于短 TR（即 TR ≪ T2 < T1），信号强度公式可以进行简化，因为 E1 ≈ 1 - TR/T1，并且 E2 ≈ 1 - TR/T2。那么射频脉冲符号交替平衡稳态自由进动序列的信号强度公式可以表述成 T1/T2 的函数：
Because the factor of T1/T2 is in the denominator of Eq. (14.25), balanced SSFP is sometimes said to have 'T2/T1' contrast weighting. This explains the hyperintense signal from fluids and fat often seen on balanced SSFP images. The signal in Eq. (14.25) is maximized when the flip angle is:由于因子 T1/T2 在公式（14.25）的分母上，那么有时就说平衡稳态自由进动序列具有 “T2/T1” 权重。这就解释了平衡稳态自由进动序列图像上液体与脂肪为什么表现为高信号。公式（14.25）表达的信号强度达到最大时的翻转角为：
At flip angles near 90°, cosθ ≈ 0, so balanced SSFP becomes more highly T2/T1 weighted because Eq. (14.25) reduces to:当翻角接近 90° 时，cosθ ≈ 0，那么平衡稳态自由进动序列获得的 T2/T1 权重更重，因为方程（14.25）变为：
为什么 T2/T1 权重更重呢，因为 1-cosθ 更大，1+cosθ 更小。
The signal in Eq. (14.27) reaches a maximum of nearly M0/2 when T2 = T1, independent of TR. This is an extremely strong signal for a short TR pulse sequence, which helps to explain the popularity of balanced SSFP methods. Balanced SSFP methods have virtually replaced the use of SSFP-echo, which also provides images with bright fluid but which produces much less signal and has greater sensitivity to flow dephasing. That is why SSFP-echo is not emphasized in this book.
当 T2=T1 时，公式（14.27）所代表的信号强度接近其最大值 M0/2，与 TR 无关。对于短 TR 脉冲序列来说，这是一个非常强的信号，这也间接说明了为什么平衡稳态自由进动序列很受欢迎。平衡稳态自由进动序列实际上已经取代了 SSFP-echo 序列的使用，在 SSFP-echo 序列图像上液体也亮，但它的信号强度相对要低得多，且对流动导致的散相更敏感。这也是在本书中我们没有着重讨论 SSFP-echo 序列的原因。
The approach to steady state in a balanced SSFP pulse sequence can take on the order of four to five times T1. This is a long time to wait relative to TR, so accelerating or catalyzing (Scheffler 2003) the approach to steady state is an important practical problem.
Moreover, once the steady state is established it often has to be interrupted, for example, for the periodic application of chemical saturation pulses or to resynchronize the pulse sequence with a detected cardiac trigger.
A simple and relatively effective catalyzing method for sign-alternated balanced SSFP is to apply a half-flip angle pulse with a half-TR interval, that is,
. More sophisticated catalyzing methods such as linearly ramping up flip angle are described in Le Roux (2003) and Hargreaves et al. (2001).
Also the SSFP can be temporarily stored on the longitudinal axis (Scheffler et al. 2001)
for the application of a chemical saturation or other magnetization-preparation pulse
by ramping down the flip angle, for example, by applying the following train of RF pulses:平衡稳态自由进动序列达到稳态可能需要花费大约 4~5 倍的 T1 值时间。相对 TR 来讲，这一等待的时间太长了，因此加速或催化（Scheffler 2003）稳态的形成是一个重要的实际问题。此外，稳态一旦建立还常常去打断它，例如施加周期性化学饱和脉冲或联合心电同步触发扫描时。对于射频脉冲符号交替的平衡稳态自由进动序列的一个简单且相对有效的催化稳态的方法是施加 θ/2 的射频脉冲，然后等待二分之一 TR 时间再施加后续的脉冲，也就是，。更复杂的催化稳态的方法比如 Le Roux（2003）与 Hargreaves et al.（2001）中提出的线性斜升翻转角。另外，为了施加化学饱和脉冲或者磁化准备脉冲，还可以通过斜降翻转角来暂时将 SSFP 储存在纵向（Scheffler et al. 2001），例如施加下述射频脉冲链：
Department of Radiological Sciences David Geffen School of Medicine at UCLA稳态一旦建立还常常去打断它，此即为 FFE 与 TFE 的概念：
【MR技术/序列研究】BFFE 与 BTFE 有什么区别？
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