T-one insensitive steady state imaging: A framework for purely T2-weighted TrueFISP



A new conceptual framework called T-one insensitive steady state imaging is proposed for fast generation of MR images with pure T2 contrast. This is accomplished by imaging between nonequally spaced inversion pulses, with the magnetization vector alternatively residing in states parallel and antiparallel to B0 for durations TPi and TAi, respectively. With TPi and TAi adequately chosen, identical signal time evolution can be obtained for different T1 values, i.e., T1 contrast can efficiently be removed from resultant images. As a specific realization of this principle, T-one insensitive steady state imaging sequences are presented which use True free induction steady precession readout blocks between the inversion pulses. While the conventional True free induction steady precession signal time course would be determined by both T2 and T1, a pure T2 dependence is realized with successfully suppressed influence of longitudinal relaxation, and images with essentially T2 contrast alone are obtained. Analytical expressions are provided for the description of the ideal signal behavior, which help in creating pathways for sequence parameter optimization. The performance of the technique is analyzed with Bloch equation simulations. In vivo results obtained in healthy volunteers and brain tumor patients are presented. Magn Reson Med, 2012. © 2011 Wiley Periodicals, Inc.

MR sequences with short pulse repetition time (TR), full gradient refocusing, and coherent echo formation have gained considerable clinical value due to their intrinsic high signal-to-noise ratio efficiency. The technique was first described for MR imaging as free induction steady precession (FISP; Ref.1), later denoted as TrueFISP to differentiate between rephased and partially dephased variants (2, 3), and is now often dubbed as balanced steady state free precession. For its signal in the steady state, analytic formulations can be found in early publications (4–11). For example, with short TR and TR << T1,T2, the steady state signal becomes dependent on the ratio of T2 and T1. This contrast, however, is not useful in many applications. For example, in brain imaging, the TrueFISP contrast between cerebrospinal fluid and parenchyma is high, but it is rather poor between gray and white matter (2), and it might be difficult to detect lesions with both elevated T1 and T2. Though TrueFISP has been used in studies that aimed at “T2-like” contrast, the authors implied that it should actually be considered dependent on T2/T1 (3, 12).

While these findings hold true for the steady state, a mixed contrast is generated in situations when central k-space data are acquired before the steady state is reached, as for instance in two-dimensional imaging with short imaging times. For this situation, it was observed that the contrast changes in a smooth way from spin-density-weighted to T2/T1-weighted (13). Specifically, it is determined by the transient TrueFISP signal, which—after suitable preparation or catalyzation to avoid signal oscillations (14–16)—shows exponential behavior and dependence on T1, T2, and the flip angle (17) and can be described by closed mathematical formulations (18–21). As it would clearly be useful to achieve (or increase) T2-weighted contrast in many clinical situations, researchers have proposed sequences that are not pure TrueFISP acquisitions and show modified contrast behavior. For example, a T2 preparation module—first reported in the context of coronary imaging (22)—was used prior to the TrueFISP acquisition (23, 24). This leads to a situation where pure T2 contrast is generated directly after the preparation, at the expense of reduced signal-to-noise ratio. In Addition, while the initial contrast ideally is T2-weighted, the evolution during the subsequent acquisition is also significantly influenced by T1. In a different approach, called T2-transition into driven equilibrium (TIDE), T2 contrast is created within a TrueFISP sequence: A 90 and a series of 180° pulses are used at the beginning of the acquisition, and thereafter, the flip angle is ramped down to a predetermined target value (25). Here, the signal evolution begins with a fast T2 decay (as would be expected from the similarity to a TSE or HASTE sequence). With decreasing flip angle, however, the T1 influence becomes increasingly prominent during the evolution to the TrueFISP steady state of the target flip angle. In both cases, the early introduction of T2 contrast induces a quick loss of signal, and T1 effects become more evident during the subsequent signal evolution, so that an acquisition interval of only limited duration can be used, if T2 contrast is desired.

Contrary to these approaches, which essentially aim to increase T2 weighting, we present a method that we call T-one insensitive steady state imaging (TOSSI), where we aim to reduce or eliminate T1 contrast (26, 27). In this concept, signal from longitudinal relaxation is allowed to enter the imaged signal, but T1 contrast is eliminated throughout the acquisition via a train of nonequally spaced 180°-pulses that are inserted into the sequence. Thus, when applied to TrueFISP imaging, images with essentially pure T2 contrast can be obtained in a short, high signal-to-noise ratio acquisition.

The general principle of the TOSSI concept is explained below, and analytic expressions are derived for both the ideal signal evolution and the calculation of optimal delays between inversion pulses, which can be used as a basis for further sequence optimization. The behavior of the magnetization is modeled using numerical simulations of the Bloch equations. Moreover, data acquired in healthy volunteers and patients with brain tumors demonstrate that TrueFISP images with T2 contrast comparable to traditional TSE approaches can be acquired within short imaging times.


In this section, basic considerations and simulations based on the Bloch equations are used to introduce the fundamentals of the TOSSI concept. First, to introduce properties of a train of inversion pulses, separated by alternating intervals TP and TA, and to prepare the concept of a continuously varying TP/TA pattern, a general description is derived from a situation of free relaxation: It is shown that such a pulse series efficiently locks the longitudinal magnetization around a value Mz that is independent of T1 which in turn means that T1 effects can be removed in medium term for a certain value of Mz using the appropriate TP/TA ratio. Hence, if Mz changes during a TOSSI acquisition due to non-T1 influences, a TP/TA ratio continuously adapted to the corresponding evolution of Mz can maintain T1 independence. Moreover, the concept of inserting TrueFISP as a readout module in between the inversions is proposed and analyzed. Starting from the transient TrueFISP signal behavior and incorporating the assumption that T1 influence can be efficiently eliminated, a function is developed for the ideal TOSSI signal evolution. Finally, using a close-up look at both this idealized function and a real TOSSI signal curve, optimized temporal inversion patterns are derived.

Throughout, radiofrequency (RF) pulses are considered as infinitesimally short, and the MR signal is expressed as the transverse component of the available magnetization M0, i.e., it is normalized to a maximum value of M0. In this article, the analytic description is confined to on-resonant behavior.

Basic Concept

The central concept behind TOSSI involves a basic mechanism of longitudinal relaxation: If a magnetization vector M resides in an orientation with negative longitudinal component Mz, i.e., antiparallel to B0, the magnitude of Mz will be reduced during longitudinal relaxation. If, however, M is oriented parallel to B0, the magnitude of Mz will grow in amplitude until it equals M0. Hence, we propose that it is possible to compensate the respective changes in the magnitude of Mz by alternately keeping M in antiparallel and parallel orientations, and to eliminate the midterm influence of T1.

For a magnetization vector of a specific length, the rate of relaxation is “faster” when Mz is negative when compared to a situation with positive Mz. Hence, it might intuitively be expected that the goal of T1 insensitivity may be achieved, when M resides in the antiparallel state for a longer time when compared to the parallel direction. The simplest way this condition can be created is using a train of nonequally spaced inverting RF pulses.

Train of Nonequidistant Inversion Pulses: Bloch Simulations

A train of 180° inversion RF pulses applied to a magnetization M (for now without any additional spin excitation or signal acquisition), alternately separated by delays TP and TA, leads to a remarkable behavior: After a sufficiently high number of pulses, the temporal evolution of M converges toward a dynamic steady state of the magnitude of its longitudinal component Mz that is essentially independent of T1. The magnitude remains close to a mean value Mm, and relaxation takes place around this value with identical time courses within each of the intervals TA and TP, respectively. For TP > TA, Mz will point in the direction of B0 during TP (“parallel”) and in the opposite direction during TA (“antiparallel”), as expected.

This concept was tested with numerical simulations of the Bloch equations using Matlab (MathWorks, Inc., Natick, MA, USA). Specifically, the dynamics of Mz after 1000 inversion pulses—used to ensure that the “locked” condition is established—was modeled for a wide range of physiologically relevant T1 times and various ratios R = TA/TP. In Fig. 1, simulation results are plotted for two considerably different T1 times of 200 and 3000 ms. Comparable simulations for intermediate T1 times would give rise to curves which fall between the two examples presented. Different R values were generated by keeping the sum of TA and TP constant at 48 ms, while adapting TP and TA accordingly.

Figure 1.

Bloch simulations: dynamic steady state of the evolution of Mz for a train of inversion pulses that are alternately separated by delays TP and TA. Time courses of (top) Mz and (bottom) |Mz| are shown for (a) R = 1 (Mm = 0), (b) R = 1/2 (Mm = 1/3 M0), (c) R = 1/3 (Mm = 1/2 M0), (d) R = 1/5 (Mm = 2/3 M0).

As can be seen, the magnetization approaches the same Mm values for each TA/TP ratio, even for considerably different T1 times. Small differences in the curves exist as faster relaxation with shorter T1 that gives rise to more prominent “zigzag” pattern around Mm. However, these results highlight the basic principle of TOSSI: Even though the T1 values of these two species differ by a factor of 15, most of the difference (i.e., the contrast) between them has been removed while maintaining high magnetization throughout the pulse sequence.

Train of Nonequidistant Inversion Pulses: Basic Considerations

The findings described above can easily be formulated in an analytical manner. The dynamic steady state is established when the loss of |Mz| during TA and the gain of |Mz| during TP compensate each other. This situation is illustrated in Fig. 2. With the assumption that Mm in good approximation corresponds to the value of |Mz| in the center of the intervals TA and TP, respectively, the evolution of Mz can be described by the following steps:

equation image(1)
equation image(2)
equation image(3)
equation image(4)
equation image(5)
Figure 2.

Schematic display: dynamic steady state of the evolution of Mz for a train of inversion pulses that are alternately separated by delays TP and TA.

Here, TP and TA represent the evolution times in the antiparallel and parallel orientations as shown in Fig. 2, while Mf and Ma represent the magnitude of the longitudinal magnetization at the times “a” and “f”. The equilibrium state sketched in Fig. 2 is reached, when the condition |Mf| = |Ma| = Mm is fulfilled. From Eqs. 15, the following expression can be obtained for Mm:

equation image(6)

For TA << T1, the approximation exp(−TA/T1) ≅ 1 − TA/T1 can be substituted into Eq. 6 (as can 1 − TA/TP, by analogy for the exponential terms involving TP), and Mm becomes

equation image(7)

As TA and TP << T1, the second-order term TA * TP may be eliminated, and Mm can be rewritten as:

equation image(8)

Note that, under these conditions and if the approximations are valid, Mm is independent of T1.

Optimum TA/TP Ratio for T1 Compensation

From the above analyses, a reciprocal conclusion can be drawn by inverting the explanation: If the longitudinal magnetization component has a specific value Mz, this amount of longitudinal magnetization can be conserved by a train of nonequidistant inversion pulses, independent of T1. The optimum TA/TP ratio, Ropt, to remove the long-term influence of T1 relaxation on the magnitude of Mz can be determined by inverting Eq. 8:

equation image(9)

This expression is in very good correspondence with the simulations shown in Fig. 1. Though it had been derived graphically for TP > TA, it also correctly reflects the special case of R = 1, where Mz passes the zero axis during each relaxation period, and is turned back into antiparallel orientation by each inversion pulse.

Moreover, if the concept is used in combination with imaging sequence readout blocks in between the inversions, the magnetization is additionally subjected to the influence of the RF pulses and transverse relaxation, and will change over time. Hence, the optimum ratio TA/TP that serves to eliminate the influence of longitudinal relaxation will also become time-dependent:

equation image(10)

If a temporal signal course is considered that is independent of T1, the image contrast will be generated by the remaining parameters that determine the contrast behavior of the sequence, e.g., transverse relaxation. With the Mz(t) of a specific target T2 time inserted in Eq. 10, a function R(t) value should be obtained that should provide an efficient separation of T2 components close to the chosen target T2 value. In the following, this hypothesis is analyzed for an implementation that uses TrueFISP as the readout sequence during TA and TP.

TrueFISP: Signal Behavior in the Transient Phase

In standard TrueFISP imaging, the on-resonant magnetization vector approximately evolves on a cone with angle α/2 to the z axis, where it is flipped from one side to the other by successive RF pulses (14, 28, 29). The transient signal can be expressed by (30):

equation image(11)

Here, after preparation of the magnetization vector to the cone with angle α/2 with respect to the z axis (14), the signal time course starts at

equation image(12)

and evolves smoothly with an apparent relaxation time constant T1* (19, 21, 30) given by

equation image(13)

It converges toward its steady state signal Sstst which can be approximated by (8):

equation image(14)

In the TrueFISP steady state, the loss of magnetization caused by transverse relaxation within each TR interval is compensated by a corresponding gain originating from longitudinal relaxation. For an actual signal smaller than the steady state signal, the evolution toward Sstst is part of the TrueFISP signal time course in an inversion recovery experiment, with a 180° pulse preceding the α/2 preparation (14). It is also described by Eq. 11, when a value of

equation image(15)

is inserted for the initial signal. Per convention, negative signal values are used in this article to describe TrueFISP signal with negative Mz.

TOSSI: Idealized Signal Curve with TrueFISP Readout Blocks

For a TrueFISP-based TOSSI implementation, inversion pulses are inserted into the TrueFISP sequence in nonequally spaced fashion to remove the influence of longitudinal relaxation, with imaging data acquisition alternatively taking place in states that are oriented parallel and antiparallel to B0. Hence, starting with parallel orientation, the resulting signal evolution ideally would reflect the transient signal of a TrueFISP experiment, but with its T1 dependence removed. To derive an idealized (albeit not realizable) function for such a signal evolution, the hypothesis must be incorporated that longitudinal relaxation is eliminated completely. This assumption can be mathematically introduced into Eq. 11 by setting T1 to infinity (i.e., T1 → ∞) in Eqs. 13 and 14. As a result, the first term in Eq. 13 vanishes, and the steady state signal in Eq. 14 becomes zero, so that the following simple expression is obtained for the idealized TOSSI signal time course:

equation image(16)

From this equation, it can be seen that the transverse magnetization decays significantly slower for TOSSI as compared to free relaxation or an ideal TSE acquisition with 180° refocusing pulses. While the signal of a TOSSI acquisition is scaled with an additional factor sin(α/2), its contrast with a specific effective TOSSI echo time TEeff,TOSSI (i.e. the time span between the start of the echo train and the acquisition of k-space center) should correspond to that of a TSE acquisition with an echo time of

equation image(17)

In TrueFISP-based TOSSI, the signal should evolve closely along the idealized curve given by Eq. 16. In analogy to the case of free relaxation shown in Figs. 1 and 2, however, as Mz is alternately oriented toward positive and negative z direction, the real signal will show fluctuations around the idealized time course. It will be constituted of “pieces” that alternately originate from the corresponding transient TrueFISP and inversion recovery (IR)-TrueFISP curves and cross the idealized function from below and from above. If the real signal curve is supposed to cross the idealized curve at an arbitrary time t′, its slope at this point is solely determined by the actual magnetization state. Specifically, it will correspond to the slope of the transient TrueFISP or IR-TrueFISP signal time curve in exactly the same state, i.e., at the identical signal value (Fig. 3). These slopes can be graphically obtained from points in time where the respective signal values amount to STrueFISP = STOSSI(t′) (Fig. 3, arrow A) or SIR-TrueFISP = −STOSSI(t′) (Fig. 3, arrow B), depending on whether M is in the parallel or antiparallel phase, respectively. Within each short TP and TA section, the signal dynamics will be driven by both relaxation and RF pulses, leading to a subtle oscillatory pattern. One might expect that different values for the TA/TP ratio may be optimal along the TOSSI curve, but its dependency on parameters such as T1, T2, and flip angle is yet to be determined.

Figure 3.

Schematic display of an idealized TOSSI signal time course (blue and solid). At a specific time t′, where the real signal curve is supposed to cross the idealized curve, the true evolution (i.e., its slope) is determined by the behavior of the corresponding transient TrueFISP (red and solid) or IR-TrueFISP (green and solid) curves, depending on whether Mz is oriented in positive or negative z direction. In specific, the slope can be graphically obtained as the tangents of these curves at time points with identical signal magnitudes, i.e., where the values of STrueFISP (arrow A) or SIR-TrueFISP (arrow B) are equal to those of STOSSI(t′) or STOSSI(t′). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Derivation of Optimized Temporal Patterns

On the basis of the considerations above, optimized temporal schemes can be determined by analyzing the slopes of the ideal TOSSI function and the transient TrueFISP signal evolutions. The question is which combination of TA and TP would lead to complementary deviations at a specific point in time. With the assumption that the intervals TA and TP are short compared with the relaxation times, a linear approximation of the exponential signal evolution is valid, and the ideal TOSSI function as well as the real signal during TA and TP may be approximated by linear functions over time. If both possibilities of a parallel or antiparallel orientation are assessed simultaneously at a specific time point t′ of the idealized TOSSI curve, the real signal curves (i.e., the tangents from STrueFISP and SIR-TrueFISP), can be considered to cross the TOSSI curve in the middle of either the TA or the TP interval. This is sketched in Fig. 4, which represents a close-up view of Fig. 3 at time t′. The slope of each linear function will be determined by the first derivation of the respective exponential time course. In specific, the slope of the TrueFISP evolution amounts to

equation image(18)

This formulation is valid irrespective of the value of S0, i.e., Eq. 18 holds true for both TrueFISP as well as other schemes such as IR TrueFISP. For the ideal TOSSI curve, the slope can be calculated as

equation image(19)
Figure 4.

Schematic close-up view of an idealized TOSSI function (blue) and two corresponding “pieces” of actual signal courses, as they would occur around a time point t′ in a real TOSSI signal evolution during a parallel (red) or antiparallel (green) phase. The slopes of these real signal curves match those of corresponding transient TrueFISP or IR-TrueFISP evolutions at identical signal values. An optimal ratio of TP/TA can be derived by inserting the condition that the deviations ΔSP and ΔSA compensate each other. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

The slopes during mA and mB correspond to slopes of TrueFISP curve, but not to those at the time t of interest, but for those times where the signal matches that of the TOSSI signal at time t. Hence, mP is retrieved by inserting STOSSI(t) in Eq. 18, which results in

equation image(20)

The slope mA, however, is retrieved by inserting the negative value −STOSSI to consider the TrueFISP situation with negative Mz, and after multiplication with −1 to treat the signal curve as mirrored into the positive range:

equation image(21)

It can easily be shown that the relation

equation image(22)

holds true for α/2 < 90°, i.e., the real evolution is steeper than that of the ideal TOSSI curve when M is antiparallel, and that it is less steep when parallel to B0. The deviations of the real signal evolution from the ideal TOSSI signal (before and after crossing it) induced in parallel state and in the antiparallel state can be expressed by

equation image(23)
equation image(24)

The ideal TA/TP ratio, Ropt, for balancing the signal along the ideal TOSSI curve is found when both signal deviations match:

equation image(25)

so that Ropt can be written as

equation image(26)

After insertion of Eqs. 1921 and using Eqs. 13 and 14 for Sstst and T1*, this expression reduces to

equation image(27)

For magnetization on the α/2 cone, transverse, and longitudinal magnetization relate to each other as

equation image(28)

Hence, the longitudinal component of M can be expressed as

equation image(29)

The comparison of Eq. 27 with the ideal TOSSI curve yields:

equation image(30)

This directly corresponds to Eq. 10 which had been derived in a more general fashion from the free relaxation situation. With Eq. 27, it is now possible to derive optimized temporal schemes for subsequent times TP and TA at a certain flip angle for components with T2 times around a certain T2 of interest.


From the analytical calculations of relaxation characteristics, temporal patterns were derived for the design of TOSSI acquisition schemes. Typically, values between 75 and 125 ms were used as the target range for T2, corresponding to values expected for brain parenchyma. Numerical simulations of the expected signal evolutions, based on the Bloch equations, helped to investigate and further optimize the magnetization time course behavior of specific sequence embodiments. For simplification, both RF pulses and signal acquisition were assumed infinitesimally short.

To assess the influence of the resulting signal curves on spatial encoding and image resolution and to investigate the influence of the off-resonant behavior, additional simulations were carried out for gray matter (GM) and fat. For these tissues, T1/T2 values were assumed to be 1165 ms/92 ms (30) and 343 ms/58 ms (31), respectively. For fat, an off-resonance frequency of 220 Hz was used (assuming 1.5 T), which corresponds to a dephasing angle of 152° over the TR interval of 6.46 ms. From the simulated signal curves, corresponding point-spread functions (PSFs) were calculated by zero-filling the data to 4096 points, a subsequent Fourier transformation and a normalization to a maximum value of 1 for the PSF of GM.

For a first actual implementation, multiple TOSSI sequence variants were implemented on a 1.5 T clinical MR system (Magnetom Vision, Siemens Healthcare Sector, Erlangen, Germany). The basis for the imaging blocks was a standard TrueFISP sequence, with NA and NP acquisition intervals during the antiparallel and parallel imaging block, respectively. As depicted in Fig. 5, each block was prepared with an α/2- and concluded with a −α/2-pulse (14, 28) to maintain smooth transient state conditions on either side of the inversion pulses.

Figure 5.

TOSSI sequence implementation: schematic display of the general pattern of TA and TP periods, with inversions pulses (180°) in between, surrounded by gradient spoilers (Sp). The timing of a single TrueFISP imaging block with α/2 preparation and flip-back modules is illustrated. Note that NA acquisitions take place during TA, whereas NP acquisitions are carried out during TP (not shown for the latter).

Due to software constraints on the scanner used in these experiments, it was only possible to implement the TOSSI concept with constant values for NA and NP, i.e., with constant TA/TP ratios. Single-shot TOSSI sequences with linearly incrementing phase-encoding steps were realized and tested with different timing schemes. To account for the inverted state of the magnetization vector during the TA periods, the respective data were scaled by −1.0 before reconstruction.

To demonstrate the contrast achievable with TOSSI, the method was tested and optimized in healthy volunteers, and a small study was conducted in patients with brain tumors. All human studies were performed in accordance with the local ethics committee. Informed consent was obtained from all subjects. In all experiments, the standard head coil of the system was used for both RF pulse transmission and MR signal reception.

In the patient study, images with standard TrueFISP and T2-weighted TSE sequences were acquired as contrast references. The most important imaging parameters are listed in Table 1. For TOSSI, a scheme with NP = 23 and NA = 8 was selected which corresponded to TP and TA values of 169 ms and 72 ms, respectively. This pattern was replicated eight times to acquire a total of 8 * (23 + 8) = 248 phase-encoding steps, so that a single-shot TOSSI image was acquired in an imaging time of 8 * 241 ms = 1928 ms. The center of k-space was sampled in the middle of the third TP interval which corresponded to an effective echo time of 586 ms. For the standard TrueFISP and TSE acquisitions, linear and linear segmented phase-encoding schemes were used, yielding effective echo times of 824 ms and 98 ms, respectively.

Table 1. Imaging Parameters of the TrueFISP, TOSSI, and T2-Weighted TSE Protocols
  • a

    Please note that generic terms have been used in this table to compare corresponding quantities. While the echo distance (time between adjacent RF pulses) is typically dubbed TR in a TrueFISP acquisition, the effective TE (time from start of the echo train to acquisition of k-space center) corresponds to the standard TE in a TSE protocol. The value of TR in this table denotes the time from shot to shot, which is the standard nomenclature in TSE sequences, but not applicable to the single-shot acquisitions with TrueFISP or TOSSI.

Excitation/refocusing angle (°)5050180
Slice thickness (mm)888
FOV (mm)256256256
Reconstructed matrix (zero filled)256256256
Acquired matrix256248242
PE lines per shot25624811
Number of shots1122
Receiver bandwidth/(Hz/pix)488488130
Echo distance (ms)a6.466.4616.54
Effective TE (ms)a82458698
Echo train duration (ms)16541928192
TR (ms)an.a.n.a.3000
Scan time (s)1.6541.92866


Simulations and Optimizations

In Fig. 6, TrueFISP and TOSSI signal time courses are depicted for a flip angle of 50°, together with the corresponding TA/TP ratio evolutions. Data are shown for different T2 values: For short T2 times between 75 ms and 125 ms as encountered in the brain, and for a longer value of 1000 ms which could represent a fluid compartment. For each T2, a considerable range of T1 values was simulated (800, 1200, and 3000 ms). Whereas Fig. 6a shows simulated signals for TrueFISP, Fig. 6b depicts the ideal TOSSI curve given in Eq. 27. In Fig. 6c,d, results of Bloch simulations are displayed for a TOSSI scheme with constant TA/TP ratio as described in the “Materials and Methods” section, and for a flexible TOSSI scheme that was designed for the separation of signal from compartments with different short T2 values, like those of white and GM of the human brain. As can be seen, the standard TrueFISP signal time courses shown in Fig. 6a depend on both T2 and T1, and curves with an identical T2 but different T1 cross each other. The TrueFISP acquisition can be interpreted as a special case of TOSSI with just a single P block. This corresponds to TA = 0 or TA/TP = 0 which is displayed as a single black dot on the right side of Fig. 6a. This value is far away from the ideal TA/TP ratio evolutions of Eq. 27 that are visualized in the same colors as the signal curves on the left. In Fig. 6b, the ideal TOSSI signal evolutions as given by Eq. 16 are plotted over time. Here, the different T2 components are clearly separated throughout the plot, independent of T1.

Figure 6.

Results of simulations and optimizations: Signal evolutions (left, colored), ideal TA/TP functions (right, colored), and actually simulated TA/TP (right, black dots) for Standard TrueFISP (a), ideal TOSSI according to Eq. 16 (b), TOSSI with constant TA/TP (c), and TOSSI with varying TA/TP (d).

In Fig. 6c, the TOSSI signal time courses are plotted for a scheme with constant TA/TP of NP = 23 and NA = 8—the same as was implemented on the MR system and used for the in vivo experiments. As can be seen, this scheme is suboptimal in that considerable fluctuations of the signal amplitude are created. However, different T2 values are reasonably separated, and T1 influence is reduced in comparison to the TrueFISP curves. On the right side of Fig. 6c, the used TA/TP is plotted over time. Here, the time points were attributed to the middle of the intervals spanned by each pair of adjacent TA and TP or TP and TR. For the start of the curves at t = 0, the assumption was made that all signal curves start with a common value which would correspond to a point where the ideal TOSSI curve and the actual signal course intersect. Hence, the value of first TP was doubled for the calculation of the first TA/TP ratio, leading to a reduced value for the first TP and TA combination. From the simultaneous display of ideal continuous and used discrete TA/TP, it becomes apparent that this scheme is not optimal throughout the complete time course.

In Fig. 6d, simulation results are displayed for a flexible TOSSI scheme with varying TA/TP that was optimized for a T2 value of ∼100 ms. Specifically, the scheme for {NP1/NA1, NP2/NA2, NP3/NA3,…NPi/NAi} was {20/4, 19/4, 12/4, 10/4, 9/4, 8/4, 7/4, 7/4, 6/4, 6/4, 6/4, 5/4,…, 5/4}, respectively. A constant TA was used to render a monotonously increasing evolution of TA/TP possible, and—as illustrated on the right side of Fig. 6d—TP was chosen such that the successive discrete TA/TP values (black dots) matched the continuous ideal TA/TP (colored lines) as well as possible. As the latter appear to be very similar for the different short T2 times, an optimization for an intermediate T2 shows to work well for a wider range of similar T2 times. As shown in the left, the ideal signal curve is closely reproduced by simulated curves with optimized varying TA/TP, and the fluctuations are significantly reduced in comparison to the pattern of Fig. 6c. The T2 values are separated effectively independent of the respective T1, and essentially pure T2 contrast is generated.

In Fig. 7, calculated and simulated signal evolutions and corresponding PSFs are shown for GM and fat. For both, the idealized signal curves according to Eq. 16 show smooth exponential signal decay (Fig. 7a, top), and hence, the related PSFs are reflected by Lorentzian functions (Fig. 7b,c, top), with a full width at half maximum of 1.94 pixels for GM. The corresponding real signal curve features small fluctuations (Fig. 7a, bottom), but these do not have a substantial negative impact on the PSF. Here, the full width at half maximum amounts to 1.86 pixels, i.e., some degree of spatial blurring is expected for single-shot TOSSI acquisitions. For fat, however, the considerable off-resonance dephasing leads to a disturbed signal curve with prominent oscillations (Fig. 7a, bottom), and hence, to notable irregularities and sidebands in the corresponding PSF (Fig. 7b,c, bottom, arrows). These imply a spatial dislocation of a fraction of the fat signal, which could lead to image artifacts.

Figure 7.

Results of simulations for GM, solid line, and fat (dotted line). Signal time courses (a) and corresponding PSFs plotted over different pixel ranges (b,c) for the idealized TOSSI behavior of Eq. 16 (top) and for TOSSI with varying TA/TP (bottom). While the fluctuations in the GM signal curves show not to have a prominent effect on the PSF, the disturbed signal curve for fat is associated with markable problems in the PSF (arrows).

In Vivo Studies

In Figs. 8 and 9, in vivo results obtained in tumor patients are shown. In each case, the TrueFISP image is shown on the left, the single-shot TOSSI image in the middle, and the T2-weighted TSE image on the right. While gray and white matter show nearly uniform amplitude in the standard TrueFISP image, the TOSSI image exhibits essentially pure T2 contrast, very similar to the corresponding T2-weighted TSE image. Specifically, blood is dark and subcutaneous fat appears artificially bright in the TSE images, as known from the literature (32). In the TOSSI data, however, blood is shown with comparatively high and fat with low signal, a result which more correctly reflects the T2 values of these compartments.

Figure 8.

Images obtained in a patient with cystic brain metastases (primary tumor ovarian carcinoma): TrueFISP (left, TA < 2 s), TOSSI (middle, TA < 2 s), and T2-weighted TSE (right, TA = 66 s). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 9.

Images obtained in a patient with a glioblastoma: TrueFISP (left, TA < 2 s), TOSSI (middle, TA < 2 s), and T2-weighted TSE (right, TA = 66 s).

Figure 8 shows images of a patient with cystic brain metastasis. A large metastatic tumor in the occipital white matter is visible in all images. However, the surrounding edema and a much smaller lesion in the frontoparietal white matter are hardly visible in the TrueFISP image. However, both are clearly delineated in the TOSSI image, corresponding to their appearance in the T2-weighted TSE image (arrows). In Fig. 9, images of a patient with a glioblastoma are displayed. While the TOSSI image is sensitive to susceptibility effects in regions with inhomogeneous magnetic field distribution such as the nasal sinuses, it reveals fine structural details within the core of the lesion, and its contrast closely resembles that of the T2-weighted TSE image.


The calculations and simulations presented in this work demonstrate that the influence of longitudinal relaxation can be efficiently compensated with the TOSSI concept and that signal evolutions can be created which essentially depend solely on T2. With an effective elimination of T1, however, the sole mechanism for gaining back longitudinal magnetization is removed, so that the signal evolves toward zero but not toward the original TrueFISP steady state value.

The derivation of the idealized TOSSI function was based on the assumption that TA << T1 and TP << T1, a condition that cannot be easily realized in practice. Consequently, the real curves show some deviation from the idealized curve, which becomes evident as signal fluctuations. For on-resonant magnetization, however, it could be shown that the real curves evolve closely around the idealized curve and that the small fluctuations do not critically contaminate the PSF or impede spatial encoding.

From the shape or width of the PSF, it can be directly deduced that some degree of signal blurring is expected in phase-encoding direction for single-shot TOSSI. However, with flip angles significantly smaller than 180°, the resulting apparent decay times are much longer than the true T2 values. Consequently, the signal decay is less steep, and the blurring is less severe than it would be expected in a corresponding single-shot TSE-based acquisition. In fact, the TOSSI signal behavior renders the use of very long echo trains feasible and makes it possible to capture the center of k-space at rather long effective echo times to capture maximum T2 contrast. Hence, single-shot imaging proved to be possible even for comparatively large matrices, even with only moderate TR values and no use of parallel imaging.

For off-resonant magnetization such as fat, however, the situation can become problematic in that the signal curve shows oscillations and the PSF indicates considerable spatial misencoding. This might not be unexpected with the used α/2 preparation scheme that is suboptimal in off-resonant situations. It should be noted, however, that the PSFs were (per definition) calculated for object with a size of a single pixel. Hence, the intensity of the PSF corresponds to the integral of the signal curve. With increasing object size, the amplitude of the PSF will more and more correspond to the signal acquired at the k-space center. Hence, with the chosen effective echo time of 586 ms, it can be deduced from the signal curve that fat will appear with very low signal. This could be a disadvantage in situations where the presence or absence of lipids in a lesion helps in the differential diagnosis. However, we believe that there are still plenty of situations where a rapid T2-weighted scan would be useful even without an accurate fat signal visualization.

The technique presented here has the intrinsic requirement that inversion pulses have to be inserted within the imaging sequence, which means that a certain amount of time is not directly spent for the generation of MR signal. This leads to a slight reduction of the scan efficiency of the method if compared to a standard TrueFISP acquisition. Moreover, these pulses may be sensitive to inhomogeneities of B0 and B1, which could lead to local image contrast variations, and crosstalk effects might play a role in multislice imaging. Finally, these additional RF pulses lead to an increased power deposition during the data acquisition, which might be problematic at higher field strengths.

In addition, the calculations and simulations presented here have some general limitations. Within the scope of this work, several factors were neglected that are known to have impact on the TrueFISP signal. These include flow and diffusion (33) as well as magnetization transfer effects (34). Also, the influence of finite RF pulse durations (35, 36) was not considered.

On the other hand, good results were obtained in the small patient study presented in this article, but there is potential for further improvements of the method. Although essentially purely T2-weighted single-shot images were obtained even without the use of optimized varying TA/TP values, a more precise separation of similar T2 values and smoother signal time courses should be possible with a realization of optimized temporal patterns that reflect the ideal TA/TP for a specific range of T2 values. Due to the discrete nature of the TA and TP intervals, given these are composed of discrete excitations, TR intervals, and spoiler times, the ideal course of TA/TP cannot be reproduced exactly. According to the simulations presented in this work, however, approximate discrete approaches should nonetheless have high potential. Although specific implementations will never be optimal for all possible T2 times, a wide range of values can be covered, and it should be possible to find optimized schemes for various applications.

A first implementation of this more optimized approach was described in a preliminary report, where an optimized inversion spacing was used in combination with parallel imaging and adiabatic inversion pulses that facilitated multislice imaging (37). To achieve an improved PSF and to enhance the resolution of TOSSI, it was proposed to combine an initial TOSSI acquisition with a later standard TrueFISP phase within a single echo train. This approach showed to be beneficial for fast T2-weighted imaging in the human abdomen (38), and is left to be optimized and tested for other body regions; this method is the focus of a companion manuscript. Further approaches to optimize the technique might include using variations of the flip angle within the up- and down-periods, or the combination of the TOSSI principle with a preceding T2 preparation module, such that T2-weighting is already created before the signal acquisition, at the expense of some signal-to-noise ratio loss. Other aspects that remain to be investigated are the general robustness of TOSSI against off-resonance effects and the feasibility and usefulness for fast T2 imaging in more challenging applications such as cardiac imaging and interactive real-time imaging, where TOSSI was suggested as a promising approach (39).


In this study, a novel concept was presented for the generation of pure T2 contrast. Both calculations and simulations showed that it is possible to remove the influence of longitudinal relaxation from the magnetization evolution by means of nonequidistant inversion pulses, and to generate signal time courses that are solely determined by transverse relaxation. Both the initial signal and the apparent decay rate are influenced by the choice of flip angle, which makes it possible to use long echo trains, late effective echo times, and hence, to realize purely T2-weighted single-shot imaging with the complete signal evolution being governed by T2. These findings were confirmed by the results of a small study in patients with brain tumors: Single-shot TOSSI images acquired within less than 2 s revealed a contrast essentially identical to that of T2-weighted TSE acquisitions in brain parenchyma.


The authors thank Prof. Jeffrey L. Duerk for fruitful discussion and his helpful comments on the manuscript.