Delay alternating with nutation for tailored excitation (DANTE) pulse trains are used for frequency-selective excitation of a narrow frequency region in high-resolution NMR spectroscopy (1). Another important application of DANTE pulse trains is in spatial tagging of MR images (2) where a tagging gradient is played out concurrently with a series of low flip angle (FA) hard radio frequency (RF) pulses to saturate 1D bands or 2D grids of tissue signal, e.g., in the assessment of cardiac wall motion (3). Here, we introduce a novel application of DANTE pulse trains to the suppression of signal from moving spins, while largely preserving the signal from static spins.
The DANTE-prepared imaging sequence described in this work can be considered essentially as a nonselective unbalanced steady-state free precession (SSFP) module. One reason that the term DANTE is adopted rather than the term SSFP is that SSFP conventionally refers to the imaging readout sequence, whereas our proposed method uses DANTE as a flow-suppression preparation. However, a more important reason is that to describe a quantitative framework for the signal from flowing and static spins it is the transient state longitudinal magnetization that is more important than the steady state description.
Motion sensitivity of SSFP sequences has long been recognized and studied (4). Although some applications relevant to flow suppression have been proposed (5–10), the importance of SSFP mechanisms for flowing-spin signal attenuation has not been fully realized. This is likely due to the fact that standard SSFP readout imaging sequences use selective RF pulses, for which the inflow signal enhancement of flowing spins is usually much stronger than any flowing spin signal attenuation effects. Another reason is the complexity in quantification of flowing spin attenuation, given the laminar pulsatile flow patterns typical in vivo, which leads to a wide distribution of spin velocities in fluids such as blood and cerebrospinal fluid (CSF). However, flowing systems with velocities below 1 mm/s have been studied extensively by Patz (11), for which a flow dephasing parameter has been introduced to quantify the signal attenuation in SSFP.
If DANTE pulse trains can be used to suppress moving spins while retaining static signal, then one obvious application is in black blood (BB) imaging. Several methods have been used in the literature for effective BB preparation to assess vessel wall anatomy and pathology (12–17). Among those methods, the double inversion recovery (DIR) (15) and motion sensitive driven equilibrium (MSDE) (17) techniques are the two most prominent, chosen on the basis of the quality of their BB effectiveness and their image acquisition efficiency. The DIR technique is known to have reasonable BB suppression (18). However, DIR imaging acquisition efficiency is generally compromised by its requirement for single-slice sequential acquisition, due to the use of nonselective 180° pulses (17) to define the T1 null of the blood. In addition, the BB effect of DIR relies heavily on the balance between the flow velocities present and the thickness of the imaging slice. As such, it is very difficult to achieve high-quality BB multislab 3D imaging with DIR preparation due to the substantially increased outflow volume required for effective blood nulling compared to 2D imaging (18). The MSDE module has been proposed as an alternative method with more robust BB qualities to address the difficulties of multislice 2D and multislab 3D image acquisition (17). Sources of static signal loss are, however, inevitable, including inherent T2 decay, T1 steady state decay (19), and diffusion attenuation introduced by the MSDE preparation module. Some further sources of signal loss, such as eddy currents from the strong flow crushing gradients and imperfections in the MSDE module's 180° pulse(s) caused by B1 inhomogeneities, can also be present. Moreover, specific absorption rate (SAR) problems due to the employment of multiple 90° and 180° pulses significantly compromise the use of multislice MSDE preparation at high static field (17).
In this work, we aim to show that when DANTE pulse trains with short interpulse repeat times (tD < 5 ms) are applied in combination with a field gradient along the direction of flow, a significant attenuation of flowing spins is achieved. We also aim to quantify our observations with a transient-state longitudinal magnetization decay model derived via the Bloch equations. We then seek to show that the static tissue, conversely, preserves the majority of its transverse coherence despite the gradient fields applied during the DANTE pulse trains. This leads to minimal attenuation of static spins and substantial attenuation of flowing spins. By making some simplifying assumptions, we derive here an effective analytical framework for quantifying the static and flowing spin signals. This framework is then validated using both Bloch equation simulation and experimental comparison.
The proposed DANTE-prepared imaging sequence is shown in Fig. 1, indicating both the DANTE preparation module itself as well as the proposed method for embedding it within an imaging readout method, such as a turbo spin echo (TSE) sequence. TD in Fig. 1b represents the inter-DANTE module delay time, which can be either equal to or longer than the time required for the respective segment of the readout module, depending on the imaging repetition time (TR) and the number of segments measured in each TR. Proper treatment of this duration in a theoretical model of image contrast is important for rigorous quantification of the signal from moving and static spins. Figure 1a shows a train of Np low FA nonselective DANTE RF pulses of FA α, interspersed with gradient pulses of amplitude Gz.
During the DANTE module, static and moving spins differ in terms of their phase coherence. For magnetization to exhibit phase coherence, the angle between the excitation pulse and the transverse magnetization phase must be fixed from one TR to the next (i.e., zero or linearly increasing phase). Quadratic or higher order phase accumulation will result in magnetization spoiling (20). The first condition for phase coherence, then, is a fixed increment on the phase of the excitation pulse (common special cases are those of 0° increment: +α, +α, +α, … and 180° increment: +α, –α, +α, …). We additionally require that the phase accumulated by the transverse magnetization is the same in each pulse interval. Static spins will meet this condition if the gradient area during each tD is fixed (as in Fig. 1a). However, consider a spin moving with constant velocity v along the applied gradient. The location of the spin at time t is given by X(t) = X0 + vt and the phase accumulation of the flowing spins between the (n − 1)th and nth pulse is described by (20):
where Δϕ(n) is the phase accumulated between pulses at times (n − 1)tD and ntD, γ is the gyromagnetic ratio, and the simplifying assumption is made that the gradient is constant between the pulses.
This phase can then be broken into a constant phase increment (ϕ0) and a time-varying, increasing increment (nϕ1). Static spins (v = 0) will have a fixed phase increment, leading to overall linear phase accrual and are therefore phase coherent (21). Flowing spins, conversely, have an increment that increases with time (n), resulting in overall quadratic phase. This will result in a spoiling mechanism very similar to the commonly used quadratic phase cycling strategy used in RF spoiling (20). Spoiling due to quadratic phase cycling has been well studied and is known to have a strong dependence on the specific phase increment (nϕ1), with some values of ϕ1 having little effect on the magnetization (e.g., ϕ1 = 360°). This suggests that the degree of spoiling would be profoundly dependent on the flow velocity. However, as will be shown, even a small amount of velocity averaging (due to heterogeneity within a voxel) results in efficient spoiling that is remarkably independent of mean velocity. This suggests that the DANTE preparation module shown in Fig. 1a with a short pulse interval may be expected to have a significant signal attenuation effect on flowing spins.
Although the sequence in Fig. 1 is based on known magnetization dynamics, there are several important differences. First, we require a description for both static and flowing magnetization. In addition, our DANTE trains constitute transient (non-steady state) magnetization starting from an arbitrary initial magnetization. To account for these specifics, we begin with Carr's general framework for the magnetization using a matrix formalism (22). We show how this approach can be used to derive closed-form expressions for the full transient magnetization. Finally, we present useful approximations that assume the transverse magnetization is fully spoiled in the case of moving spins.
Nonflowing Magnetization: Exact Formulation
Following Carr, the magnetization evolution for static spins at the end of the nth tD period can be described using matrices representing rotations (denoted R) and signal decay (denoted E):
In Eq. , E1 = exp(−tD/T1), E2 = exp(−tD/T2), θ is the “generalized precession angle” per tD period, α is the DANTE FA, and M0 = [0 0 1]T. The generalized precession angle, θ, is the phase angle between the nth RF pulse and the magnetization immediately before this pulse. This conveniently captures both any fixed RF phase increment that may be used and off-resonance precession of the magnetization itself. For example, if the RF is applied with alternating phase (+α, –α, +α, …), and if the gradient G is on for approximately the entire tD period, and if the magnetization at position r has off-resonance frequency ω(r), then:
where π is the RF phase increment and the middle term is Eq.  with v = 0.
For a sufficiently long DANTE pulse train, the magnetization reaches its steady state (Mss) when Mn = Mn − 1. Thus, in this condition:
A matrix inversion can be used to calculate the well-known, closed-form expressions for the steady-state magnetization (see Eqs. 6–12 in (23)).
For our purposes, however, we wish to describe the transient magnetization existing at the end of a shorter train of pulses applied to an arbitrary starting magnetization, Mini, as this will describe the static tissue magnetization available to be sampled during each readout module. Starting from Mini, we have at the end of the first DANTE tD period:
and by successive application of Eq.  from this starting point, we can obtain:
This closed-form expression exactly describes the transient magnetization at the end of the nth subperiod of the DANTE pulse train for an arbitrary starting magnetization Mini. The first term in Eq.  describes how the initial magnetization decays with increasing n, while the second describes relaxation toward the steady state of Eq.  (see Appendix).
It is worth noting that the gradient (and other field inhomogeneities) will induce a range of θ across the voxel. Because the magnetization at every voxel location behaves according to its local θ, however, one can simply sum across vectors Mn(θ) to obtain the net voxel magnetization.
Flowing Magnetization: Exact Formulation
To account for magnetization with velocity v, we must modify Eq.  to encapsulate an additional rotation about z that varies according to Eq. :
where is the flow-induced phase increment term described in Eq. , and Fn = (Rz(ϕ1))n. (Note that ϕ0 in Eq.  is already accounted for in the static matrix A.)
For an arbitrary initial starting magnetization, we can follow a similar (but more involved) derivation to that of static magnetization by propagating Eq.  through multiple subperiods of the DANTE pulse train, starting from Mini, to yield:
where Π indicates a matrix product. Successive periods (increasing n) have increasing powers of the rotation matrix F. Because matrix products do not commute, Eq.  cannot generally be simplified as for the static magnetization in Eq. .
The central term in Eq.  is the product of rotated versions of the matrix A (i.e., each term FkA represents A rotated by kϕ1). For phase increments that are a small integer divisor of 360° (e.g., 90°, 180°, or even 360°), the product of rotated A matrices will retain some phase coherence and will therefore leave the magnetization largely unspoiled. In particular, if ϕ1 is an integer multiple of 360°, F is the identity matrix, and Eq.  reduces to Eq. . For ϕ1 that do not form simple multiples of 360°, increasing powers of F will be incoherent and tend to cancel each other, resulting in a net operator that spoils the magnetization. Further, the range of velocities present in any physical vessel will tend to reduce the dependence of the degree of spoiling on the exact value of ϕ1, as shown later.
It is worth briefly commenting on the serendipitous nature of the signal attenuation implied by Eq. . Most gradient-based methods for attenuating moving magnetization impart a phase profile with a linear dependence on velocity, which attenuates the signal provided the range of phases is close to some multiple of 360°. Here, the DANTE pulse train is shown to naturally induce a different kind of velocity-based spoiling, in which even a small gradient causes flowing spins to experience quadratic phase cycling from one tD period to the next. This property is remarkable in light of the fact that quadratic phase cycling has been shown to be the only phase manipulation that exactly satisfies the necessary conditions for spoiling transverse magnetization (20) (although the degree of spoiling depends on the phase increment ϕ1, as discussed above).
Nonflowing Magnetization: Approximation
The above expressions are exact for the full magnetization, and in particular make no assumptions about spoiling. However, it is difficult to gain much intuition about the signal behavior from equations in a matrix form. In this subsection and the next, we present more intuitive approximations for the resultant longitudinal magnetization by assuming full or partial spoiling of the transverse components. We focus solely on the longitudinal component as it determines the contrast available to the subsequent imaging readout module.
For nonflowing magnetization, phase coherence means that we cannot neglect the contribution of transverse magnetization to the longitudinal state. However, for small DANTE FAs, as are used in our practical implementation of this sequence, we can assume that the transverse magnetization from two or more previous periods has a negligible contribution to the longitudinal magnetization. If we relate the nth period to the (n − 2)th we note that:
and our approximation corresponds to zeroing the (3,1) and (3,2) elements of A2:
where [·] indicates quantities of no interest. Using the definitions of A and B in Eq. , we can then derive an expression for the longitudinal magnetization by calculating A2(3,3) and (A+I)B, giving:
where = A2(3,3) is an apparent T1 decay over two periods:
For large n, this approaches a pseudo-steady state (Mn,z = Mn − 2,z) given by:
Combining Eqs.  and  and assuming an initial magnetization Mini,z we finally obtain:
As above, this expression represents magnetization transitioning from its initial state toward its steady state at a rate dictated by E1,app.
Note that the value of E1,app, and hence the longitudinal magnetization that is achieved by the static spins, is dependent on the value of cos θ. Although in small part θ is modulated by the local field inhomogeneities, it is largely a function of the spatial offset of the spin in the gradient that is applied between the DANTE RF pulses, through Eq. . As such, cos θ will be spatially varying and will depend on the strength of gradient and the interpulse interval. In extreme cases, it may give a subvoxel modulation, but in general it will yield the banding pattern across the field-of-view that is a well-known property of balanced SSFP. An example of the form of banding pattern, as a function of the gradient evolution term, θ, is shown in Fig. 2. It can be seen from Fig. 2 that the form of the banding pattern depends on the FA and the total number of pulses (n = Np) applied. It can also be seen that for the low FAs used in the DANTE pattern the width of the “troughs” is quite narrow, and for the typical RF pulse separations used in this study the bands will be separated by at least 500 Hz.
Flowing Magnetization: Approximation
As discussed above, the case for flowing magnetization is quite different. The phase of the transverse magnetization accumulates quadratically over time, which will spoil the transverse component for most values of ϕ1. Although some phase increments are not spoiled, we assume for now that the transverse magnetization is completely spoiled, such that Mx = My = 0. This should be valid as in any voxel within a vessel there will be a distribution of velocities, and hence phase increments, present. There is then no need to include the matrix F, as it only affects the transverse magnetization. Combining Eqs.  and , we then obtain:
Starting from an initial z magnetization Mini,z, and propagating through Eq. , we get a progressive saturation Equation (24) given by:
As n → ∞, the magnetization will approach a steady state, given by:
As for the nonflowing spins, we can combine Eqs.  and  to arrive at a very similar expression to Eq.  for flowing magnetization:
From Eq. , it can be seen that with increasing Np (i.e., maximum n for a given DANTE train) the magnitude of Mn,z tends toward its steady state value, Mss,z, with an apparent T1 decay time given by 1/T1,app = −ln(cos α)/tD + 1/T1.
When α is a small FA, a Taylor expansion may be used to write cos α ≈ 1 − α2/2 and ln(1 − α2/2) ≈ −α2/2, such that the apparent T1 decay may be approximately expressed as 1/T1,app ≈ α2/(2tD)+1/T1. Thus, we can see that using a larger value of α is the most effective way to achieve a flow crushing effect because the 1/T1,app rate increases with the square of α. Alternatively, given a fixed DANTE pulse train duration, Np × tD, another method for effective flow crushing is to use a smaller interpulse time, tD, as this will also increase 1/T1,app. It is clear, however, that decreasing tD is not as effective as increasing α for flow crushing. It should be noted that increasing α will decrease the signal-to-noise ratio (SNR) of the static tissue simultaneously, the experimental observation of which will be detailed below. Note that Eq.  describes a velocity-independent attenuation of the longitudinal magnetization. This is a direct result from our assumption of complete spoiling of the transverse magnetization, which is borne out by simulations presented below. This means that the DANTE preparation module shown in Fig. 1 is predicted to be largely velocity insensitive, which is of great advantage for flow crushing in cases of complex flow patterns.
Hence, for both the nonflowing and flowing magnetizations we have two formulations at our disposal. First, we have the exact descriptions of the full (transverse and longitudinal) transient magnetization with no assumptions about spoiling, given by Eqs.  and . Second, we have the more intuitive approximations for the effective signal decay given by Eqs.  and , obtained by assuming that the transverse magnetization is partly or entirely spoiled.
The final consideration for actual signal calculations is the effect of relaxation during the interval TD between DANTE pulse trains. This determines the initial magnetization, Mini,z, at the beginning of a given DANTE pulse train. For simplicity, we assume that the longitudinal magnetization is not disturbed by the readout. For the flowing spins this will be approximately true, as the DANTE pulses are non-slice selective, whereas the imaging readout pulses will act only on the slice or slices of interest. If the magnetization at the end of a DANTE train is denoted Mfin,z, then the longitudinal magnetization Mini,z immediately before the next DANTE train is given by:
Equation  can then be combined with the above expressions to fully describe the time evolution of the longitudinal magnetization.
To validate the above theory against experimental data, we set out to perform a number of numerical, phantom, and in vivo experiments, as follows.
Bloch equation numerical simulations were performed to establish the velocity sensitivity of the DANTE preparation, in light of the complicated flow patterns and wide spin velocity distribution found in blood vessels due to varying vessel sizes, laminar profiles, and pulsatile flow. Code was written using interactive data language (IDL) (ITT, Boulder, CO). Two situations were modeled. First, the response was modeled of spins with a specific velocity by explicitly solving the Bloch equations described in Eqs.  and . These results were also integrated across a narrow range of velocities to study the effect of a small amount of velocity averaging. Second, a more realistic simulation was performed by modeling a super-sampled laminar flow profile of moving spins (with maximum velocity, vmax). Trapezoidal gradient pulses of amplitude Gz, played out between the component DANTE RF pulses, were assumed. In all simulations, the gradient direction was modeled as being applied along the direction parallel to flow (z). Hard RF pulses were assumed to act on all spins, with the off-resonance evolution of each spin during and between the RF pulses being calculated via its position in the gradient field at each simulated time point t. For the moving spins, T1 and T2 values of 1500 and 128 ms, respectively, were used, corresponding to values relevant to blood at 3 T. For the static spins, T1 and T2 values of 700 and 70 ms, respectively, were used. Following super-sampled simulation, net magnetization values were calculated by averaging the spin isochromats to a lower spatial resolution, to account for a realistic velocity distribution within vessel voxels. A variety of DANTE pulse train characteristics, flow velocities, and gradient amplitudes were assessed using this approach.
To demonstrate the ability of the DANTE module to preserve static spin signal and crush moving spin signal simultaneously, a flow phantom was constructed with 5 cm/s (average) tap water flowing through tubes attached to a standard phantom bottle, representing the shorter relaxation times of tissue. The relaxation time of the doped water in the standard phantom was about 100 ms for both T1 and T2. A tube containing static tap water (as marked on Fig. 4a, see below) was also attached representing long relaxation time tissue of about 2.5 s for T1 and 700 ms for T2. A standard TSE sequence was chosen as the imaging readout sequence and a Siemens 3T Verio scanner (Erlangen, Germany) was used for all experiments, along with a 12-channel head receive coil and 4-channel neck coil. Because the T1 relaxation time of water is approximately 2.5 s at 3 T, the TR of the TSE sequence was set to a rather large value of 2 s to minimize the complication of successive DANTE modules interacting with one another. Details of the phantom imaging protocols used (protocols 1 and 2) are shown in Table 1.
Table 1. Relevant Protocols for Phantom and In Vivo Validation Studies
Imaging slice acquisition
FA, α (°)
Gradient duration (ms)
TSE single slice: 2D TSE with TR/echo time = 2000 ms/13 ms; field-of-view = 150 × 150 mm2; matrix size 256 × 252 interpolated to 512 × 512; echo train length = 7; receiver bandwidth = 130 Hz/pixel; slice thickness = 2 mm; number of signal averages = 1.
TSE five slice interleaved: As for “TSE single slice” except that TR/echo time = 1500 ms/13 ms.
GRASE 3D interleaved: 3D GRASE readout with TR/echo time = 1000 ms/15 ms; field-of-view = 150 × 150 mm2; matrix size 256 × 252 × 8 for each slab interpolated to 512 × 512 × 8; turbo factor = 7; EPI factor = 3; receiver bandwidth = 514 Hz/pixel; slice thickness = 2 mm; three slabs interleaved; signal averages = 1.
TSE 22 slice interleaved: As for TSE single slice but with 22 interleaved slices and no gap. TR = 2000 ms with two concatenations.
The same 3T Siemens Verio scanner (Erlangen, Germany), fitted with a standard four-channel neck coil, was used to study seven healthy male volunteers under an approved technical development protocol (ages 24–35 years). Informed consent was obtained from all volunteers. In vivo studies were performed to validate the DANTE pulse mechanism, consisting of: (a) study of widely separated (long TD) DANTE modules with a single slice 2D TSE sequence for readout to validate the response of the DANTE preparation to an increasing number of DANTE pulses (protocol 3) and increasing FAs (protocol 4); (b) study of closely separated DANTE modules with a multislice 2D TSE sequence for readout to validate the theory under conditions of short TD (protocol 5); (c) study of the banding artifacts for the case of closely separated DANTE modules with a 3D gradient and spin echo (GRASE) sequence (TR = 1000 ms, protocol 6) and 22 slice 2D TSE sequence (TR = 2000 ms and two concatenations, protocol 7) for readout, to assess some practical BB protocols. Details of the protocols used are shown in Table 1.
In the case of these latter experiments, in which multiple slices (protocols 5 and 7) or multiple slabs (protocol 6) were acquired during the TR period, a shorter time TD between DANTE pulse trains will pertain and the effect of preceding DANTE modules must be accounted for in the theory. For the TSE experiments conducted here a fixed TSE readout period of 120 ms duration was used, i.e., the time TD for the TSE readout is assigned to 120 ms, including the time required for fat saturation. This duration allows a TSE echo train length of between 7 and 11, depending on the pixel bandwidth and SAR limitations of the protocol. The remainder of the TR time was filled with DANTE pulse preparations. In the case of protocols 6 and 7 stronger gradient moments within the DANTE train were used to limit the banding effect for practically plausible protocols.
For all sequences, an assessment of SNR and contrast-to-noise ratio (CNR) was made. Following (17), we define the SNR of the resulting image as SNR = 0.695 × S/σ, where S is the signal intensity and σ is the standard deviation of the noise. The definition of CNR is CNRml = SNRmuscle − SNRlumen. The definition for CNReff is then given by CNReff = CNRml/(TSA)1/2 where TSA is the average scan time for each slice in units of minutes.
Figure 3 shows numerical simulations of the magnetization evolution, with Fig. 3a–c being stepwise Bloch equation simulations that were found to yield identical results to Eqs.  and . Figure 3a shows a simulation of the transient evolution of longitudinal magnetization from equilibrium for a series of spins with isolated velocities of 0, 0.1, 0.5, 1.0, 5.0, and 10.0 cm/s. The following DANTE parameters were assumed: FA 7°, number of pulses per DANTE train Np = 1000, RF pulse spacing 2 ms, gradient strength 6 mT/m. Figure 3a demonstrates a distinct temporal signature for each velocity value. In particular, the time taken for the reduction in longitudinal magnetization is velocity dependent, with slower velocities maintaining high longitudinal magnetization further into the DANTE pulse train. This velocity dependence can be examined in more detail by plotting the longitudinal magnetization for a full range of simulated velocities, calculated from 0.0 to 10.0 cm/s in increments of 0.01 cm/s. The value of the longitudinal magnetization calculated at various times following the start of the DANTE pulse train is shown in Fig. 3b. It can be seen that the longitudinal magnetization is fairly unstable early in the DANTE train but soon settles down to a low asymptotic value (here, of about Mz = 0.14) across a large range of velocities. However, there is a noticeable “spikiness” to the magnetization profile as a function of velocity, with certain isolated velocities displaying fairly high levels of longitudinal magnetization. These velocities correspond to phase increments (ϕ1) that maintain some coherence throughout the DANTE pulse train.
Within a voxel, however, we do not expect perfect velocity homogeneity (nor, in fact, do we expect a given spin to experience perfectly constant velocity). If we simulate even a modest distribution of velocities by convolving the magnetization values by a simple kernel of 0.1 cm/s width, we observe the magnetization profile shown in Fig. 3c, which predicts a remarkably uniform attenuation of the longitudinal magnetization over a broad range of velocities above approximately 0.1 cm/s, and even for relatively short DANTE pulse trains.
Figure 3d and e show Bloch equation simulation results illustrating the effect of repeated DANTE pulse trains on spins moving within a simulated vessel having a laminar velocity profile and with different maximum velocities. The simulations assumed the same DANTE pulse train parameters as for Fig. 3a and b. Results are shown for peak flow velocities of 1 and 0.1 cm/s. It can be seen that for peak moving spin velocities greater than 0.1 cm/s, the signal attenuation caused by the DANTE module is approximately 80%, regardless of the maximum velocity assigned (other maximum velocity values above 0.1 cm/s showed this same attenuation). This suggests that the attenuation of signal from moving spins is relatively independent of flow velocity for values above 0.1 cm/s (1 mm/s).
Figure 4 shows imaging results acquired by setting the number of pulses (Np) to 150 and the time interval between DANTE pulses (tD) to 1 ms. A long TR of 2 s and a single slice acquisition were used to achieve a long TD, meaning that there is only one segment acquired per TR. Four of the different DANTE pulse train FAs of 0°, 4°, 6°, and 8° taken from protocol 1 are shown. It is clear that at a DANTE pulse train FA of 6° the artifact caused by flow is dramatically decreased. With a FA of 8°, under the same grayscale settings, the flowing signal has disappeared without discernable signal change of the static water signal. To quantify the moving spin signal, the assumption was made that the residual water signal in the region of interest (ROI) area of Fig. 4 would allow a reasonable quantification of flowing spin suppression between images acquired with different DANTE FAs. The area inside the residual water circle in Fig. 4d was chosen as the flow ROI, shown as the magnified image at the right corner of Fig. 4d. The quantified attenuation of static and moving spin is displayed in Fig. 5a. Additional values for the number of DANTE pulses within each train (Np = 150, 300, 600) were selected for these validation experiments (protocol 2). Theoretical curves are overlaid in Fig. 5a, calculated via Eq.  with Mini,z = 1 (full equilibrium magnetization).
In Vivo Validation
The long TR used in the in vivo validation experiments for protocols 3 and 4 make the images acquired in Fig. 6 proton density weighted images. Six datasets were acquired with a different number of pulses in the DANTE pulse train (see protocol 3) to test the fit between the theoretical model and experimental data. A DANTE FA of 5° was kept constant for all acquisitions. The determination of ROIs shown as “1” and “2” in Fig. 6 for CSF fluid and blood, respectively, was based on the image acquired with Np = 1600 because its superior CNR offered the optimal discrimination between static tissues and residual signal of moving spins. ROI “3” was chosen in the (static) muscle signal. The quantified signal attenuation curves of blood and CSF with a varied number of DANTE pulses per train are shown in Fig. 7. Both can be described approximately by Eq. .
The fit between theory and experiment for the static tissue signal is also shown in Fig. 7. For this the muscle, signal contained in ROI “3” (from Fig. 6b) was used for comparison with theory. Figure 7 shows that with a DANTE pulse train FA of 5° the muscle signal does not reach a steady state of about Mpss,z = 76% until approximately 1.6 s, i.e., after about 1600 pulses in this case. The precession angle θ (see Theory section) is dependent on the spin position, gradient amplitude, and local inhomogeneity. However, it is valid to use a calculated precession angle θ for theoretical fitting if images with different Np are acquired at the same z position. This effective precession angle was inserted into the Bloch equation simulation to yield the solid curve in Fig. 7, and into Eqs. 14 and 15 with Mini = 1 to yield the simple decay curve shown by the dotted line. Both curves agree with the measured signal intensity of muscle during this non-steady state period of the DANTE train evolution.
Comparison results between theory and experiment for protocol 4, in which the FA of the DANTE pulse train is varied, are shown in Fig. 8. Figure 8c and d show the in vivo muscle signal intensity decay (as solid squares) as a function of varying the DANTE train FA. Figure 8c shows in vivo results for Np = 300, and Fig. 8d shows results for Np = 150. The simplified model (dashed line) as well as the full numerical simulation (solid line), both shown overlaid on Fig. 8c and d, agree well with the measured signal decay. The simple approximated calculation and the full simulation of the predicted signal over a wide range of pulse train lengths for FAs of 10° and 15° are also shown for comparison in Fig. 8a and b. These show that the approximated calculation follows the envelope of the full numerical simulation curve, confirming that Eq.  simplifies the complex evolution of the partially spoiled phase in the DANTE train and gives an approximate description of the non-steady-state signal decay envelope.
Multislice images collected with a preliminary protocol that incorporates a DANTE-BB pulse train with FA = 5° and a 2D TSE readout (from protocol 5) are shown in Fig. 9. These images show an averaged SNR of muscle (SNRmuscle) in five slices of 13.3. The averaged SNR for carotid artery lumen (SNRlumen) is 1.9. The CNRml is therefore 11.4 and the CNReff is 27 min−1/2. Some residual blood artifacts in this preliminary protocol are evident, that we expect would be eliminated with a slightly higher DANTE-BB FA of 7–9°. Figure 10 shows a comparison of theory and experiment for the multislice in vivo data. Figure 10a shows a theoretical Bloch equation simulation under conditions of short TD illustrating the establishment of the respective steady state for static spins (solid line) and moving spins (dashed line). As illustrated in Fig. 10a, when repeated DANTE pulse trains with Np = 164 pulses are used, the static tissue shows little signal loss as it approaches its steady state. Conversely, moving spins fail to establish transverse coherence leading to more significant longitudinal magnetization loss. During imaging readout, both static tissue and moving spins exhibit partial recovery of longitudinal magnetization. To assess the potential for the DANTE-BB approach to allow black-blood images to be acquired under conditions of lowered blood T1 (e.g., with gadolinium on board) Figure 10b shows simulations conducted with the following parameters: blood T1 = 100 ms, tissue T1 = 700 ms, tissue T2 = 70 ms, DANTE FA = 13°, tD = 0.4 ms, Np = 136, TD = 320ms. In vivo data from the muscle ROI obtained with various FAs ranging from 0° to 7° (protocol 5, using the ROIs for signal intensity integration shown in Fig. 9) are shown in Fig. 10c. For comparison, the curve calculated from the combination of Eqs.  and  is also shown on Fig. 10c with filled squares and agrees reasonably with the experimental measurements.
For protocol 6, three slabs with eight slices in each slab were acquired with an interleaved 3D GRASE sequence. A longer tD value of 2 ms and a gradient amplitude of 6 mT/m were selected for the DANTE preparation module, with a 15° FA. This results in a banding separation Δr equal to 1.9 mm, marginally less than the slice thickness in each slab. One such slab, consisting of eight contiguous slices, is shown in Fig. 11. Uniform muscle signal intensity in each slice indicates that the banding separation is low enough to avoid significant artifact. The SNR of muscle (SNRmuscle) for the full 24 slices was measured to be 14. The averaged SNR for the carotid artery lumen (SNRlumen) was measured to be 2. Hence the CNRml is 12. By using 3D GRASE, with its higher signal acquisition efficiency than 2D TSE, the averaged imaging speed is as high as 6 s/slice. The calculated CNReff is thus 38 min−1/2, which is 30% higher than the 2D DANTE multislice experiments described above.
For the 2D DANTE-BB multislice imaging assessment, banding artifacts were minimized by selecting tD = 1 ms and a gradient amplitude of 18 mT/m, assuming a slice thickness of 2 mm. A FA ranging from 7° to 9° may then be selected. The DANTE-BB 2D TSE protocol for acquiring 22 contiguous slices in two-and-half minutes with a DANTE FA of 7° (protocol 7) was run to illustrate a clinically relevant protocol. The resulting 2D contiguous slices, reconstructed into a 3D stack using multiple planar reconstruction, are shown in Fig. 12, demonstrating that the banding artifact for this set of parameters is not evident. Figure 12a is the slice taken at location “1” in Fig. 12b. A carotid artery bifurcation image of this multiple planar reconstruction image is shown in Fig. 12b, which was taken from the location marked as “2” in Fig. 12a. A spinal cord image from the multiple planar reconstruction image is displayed in Fig. 12c, which was taken from the location marked as “3” in Fig. 12a. Both blood and CSF have been suppressed despite their very different velocities. The CNReff was determined to be 36 min−1/2.
In general, we see a good agreement between theory and experiment. The attenuation pattern for moving spins in Fig. 5a is seen to agree well with Eq. , which is derived from the Bloch equations assuming full spoiling of the magnetization following each pulse in the DANTE pulse train. An alternative simple model is to note that the short value of tD (1 ms) and the long value of T1 for water (∼2.5 s) lead to the result that exp(−tD/T1) ≈ 1, allowing the fluid attenuation in Fig. 5a to be roughly characterized by M = M0(cos α) in the regime where the TD duration between DANTE modules is long. In this case, Fig. 5b demonstrates a robust linear relationship between ln(M/M0) and ln(cos α). The slope derived by linear fitting was determined to be 157, which is about a 5% deviation from the actual value of Np = 150 used in the experiment. This suggests that the images in Fig. 4 are pure spin density images, independent of the relaxation times of the moving spins. Thus, a single measurement of the residual signal of M may be enough to determine the moving fluid proton density, M0, since α and Np are known measurement parameters. For the static spins, however, there is almost no signal attenuation due to the establishment of a transverse coherence. It is well known that the steady state magnetization for static spins (Mpss,z here) reaches a maximum value when T1 is equal to T2, which was the case of the phantom used for the data shown in Fig. 5a. In more realistic situations, there is a several fold difference between the T1 and T2 relaxation times of muscle at 3 T. This difference will cause more signal decay than is the case in Fig. 5a.
For the in vivo data shown in Fig. 7, it is noted that there is a slightly larger deviation between the theoretical prediction and experimental measurement for CSF. This is likely due to the interaction between DANTE modules given the long T1 of CSF (≈3 s at 3 T), since effectively the TD value of 2 s used in the protocol is not long enough to avoid this interaction for moving CSF. In such cases, combination of Eqs. 9 and 20 may be used for a more accurate calculation. It is well known that the flow velocity of blood in the large arteries of the neck is about 10–20 cm/s whereas the flow velocity of CSF is about 1–2 cm/s or less. The large difference in flow velocity between these two species does not cause large differences of signal decay pattern, providing further in vivo evidence for the flow velocity insensitivity of the DANTE module. This velocity insensitivity of the DANTE preparation is potentially very important in medical imaging for suppressing signal from fluids with complex flow patterns, such as blood and CSF.
One complication in using the DANTE preparation for moving spin signal suppression is that it leads to the well-known off-resonance SSFP banding effect in the slice (z) imaging direction (25). This means that a gradient applied within the DANTE pulse train along the z direction will spatially modulate Mz in that direction resulting in slice intensities with periodic intensity. In practice, there will be a maximum slice coverage that is possible without a banding artifact that can be calculated from the gradient moment and pulse interval. The separation of these bands is inversely related to the gradient moment, Δr = 2π/γtDGz, where Δr is the band separation. This modulation in static spin attenuation can be avoided by carefully adjusting the combination of imaging position and gradient amplitude (25). Alternatively, the problem can be reduced by choosing a small enough gradient amplitude such that the banding size is larger than the slice dimension field-of-view. This, however, could potentially compromise the flow crushing effect (11).
Conversely, when the gradient moment is large enough the banding separation can be smaller than the slice thickness, in which case the slice intensity is determined by the averaged signal from the banding pattern within the slice (26), as is done successfully in protocols 6 and 7. The required gradient moment to achieve this condition can be achieved with a sufficiently large value of tD. However, a larger value of tD and a consequent reduction in the number of RF pulses in the DANTE train (for fixed DANTE duration) leads to a larger value of Mss,z for moving spins, via Eq. , and hence to less BB suppression. To maintain a low Mss,z value, a larger FA is required in the protocol, which correspondingly causes lower SNR in static tissue and increases the SAR.
The theoretical and experimental validations described above show that the DANTE-BB effect can be quantitatively controlled using three experimental parameters: FA, α; number of pulses in the train, Np, and TR within the DANTE train, tD. It was found that varying the FA provides the easiest way to control the BB effect. In practice, this mechanism is more flexible and realistic than altering Np or tD. One reason is that the degree of flowing signal suppression is only linearly proportional to Np and tD but is proportional to the square of the FA. The other reason is that the value of Np is limited by the DANTE duration, which should be as short as possible to accommodate the maximum number of readout segments per unit time. Further, the BB effect should persist as blood travels through the imaging slice/slab, minimizing the effects of brief blood flow within the plane or turbulent flow patterns. None of the current BB methods have the same capability and flexibility for BB control, indicating that the DANTE-BB technique may offer advantages for clinically discriminating between residual blood signal and plaque when compared with conventional techniques.
In Fig. 12c, it is observed that there is significant signal attenuation of moving CSF fluid. Given the fast imaging speed of interleaved acquisition, this suggests that the DANTE-BB preparation may be used as an alternative method to fluid attenuation inversion recovery in imaging of spinal cord. Whereas fluid attenuation inversion recovery attenuates all fluids around the spinal cord, the DANTE sequence may allow discrimination between moving fluids and stationary fluids. This feature may offer the opportunity to observe stationary fluids, such as cysts and oedema, adjacent to moving CSF fluid.
Also, the DANTE-BB preparation appears to have minimal sensitivity to the precise velocity for values above an approximate threshold of 0.1 cm/s. This creates a good quality of BB effect even in the case of complex flow profiles found in vivo. It is worth noting that the DANTE moving spin suppression module may also have sensitivity to perfusion. In addition, it should be possible to use the approach described in this article to provide a method for quantitative relaxation time mapping of both static tissue, such as muscle and plaques and of moving fluids such as blood and CSF.
We have shown that the method can be used for flowing spin suppression in practical 2D or 3D black blood MRI, allowing accurate morphology measurement and pathology diagnosis of vessel walls. When the DANTE preparation module is used with TSE or GRASE readout modules, the overall pulse sequence becomes a hybrid sequence with the features of SSFP (static spins), RF-spoiled gradient echo (GRE) (moving spins), TSE (readout sequence), or turbo gradient and spin echo (TGSE or GRASE) (readout sequence). Additionally, unlike conventional SSFP, which lacks the ability to achieve pure T1 and T2 weighting, this hybrid sequence is able to achieve T1- and T2-weighted images by simply changing TR and echo time, respectively, in the readout spin echo sequence. Indeed, simple simulations (not shown) indicate that the effect on the static tissue Mz of the DANTE pulse train of sufficient TD with parameters used in this study modulate the signal by at most 5–10% over a wide range of biologically relevant T1 and T2 values. Thus, the majority of the signal contrast is imparted by the readout sequence. Likewise, the interlaced DANTE preparation pulse trains shown here would be preferred over a pure SSFP sequence for combined readout and BB preparation. This is because: (i) a balanced SSFP sequence would provide less BB effect than one with a residual moment (as we use here); (ii) optimizing contrast between static and flowing spins in a pure SSFP acquisition would require much higher FA than used in our studies, incurring significant SAR limitations, while the low FAs used in our preparation trains would greatly reduce the signal from static tissues (as balanced SSFP at low FA exhibits a “reversed profile” with low signal on resonance, see Fig. 3 in (22)); (iii) 2D imaging would be precluded by the use of nonselective imaging pulses; and (iv) only the standard T2/T1 image contrast would be available with SSFP readouts.
An alternative way to understand the difference between the DANTE-BB method and conventional methods is that most conventional methods either minimally manipulate the static spins in the imaging plane, such as for spatial presaturation approaches (13, 14), or immediately flip the static spins back to the longitudinal direction after preparation, such as for DIR and MSDE approaches. In contrast, the DANTE preparation method aims to manipulate both the static and moving spins optimally and simultaneously, to differentiate them via their different steady state signal behaviors. As such, the DANTE method is naturally adapted to multi-interleaved acquisition, which requires frequent repetitions of the preparation module.
In cases where an intravascular contrast agent is used, the T1 of the blood would decrease significantly, requiring altered DANTE pulse train parameters to maintain an efficient BB effect. Figure 10b shows that with a FA of 13° in the echo train, and a pulse interval of 0.4 ms, a low blood signal is possible during the image readout periods, suggesting that a BB effect could still be achieved. In general, however, the DANTE-BB preparation module uses only low FA pulses and should result in greatly reduced SAR problems at higher magnetic field strengths (3 T and 7 T). This should allow more slice or slab acquisitions to be achieved per unit time, and hence increase the time efficiency of image acquisition. Should cardiac gating be desired it should be possible to use the flexibility of the DANTE-BB module to enable this. The duration of the DANTE train is highly flexible, allowing values from below 30 ms up to an arbitrarily long time, depending on the in vivo tissue properties and imaging requirements. The repetition rate of the DANTE modules is also highly flexible, allowing values from 1 module/s to 5–6 modules/s, or higher. In the case of protocol 7, Table 1, the DANTE duration is only 64 ms, which is relatively short (noting that blood suppression would require repeating blocks of the DANTE preparation, and would not be expected after only a single isolated 64 ms preparation). We believe that with this degree of flexibility it should be possible to incorporate cardiac gating into the sequence, albeit with careful attention to maintaining a hybrid steady state. It may also be desirable for cardiac gating to use strategies to ensure a rapid achievement of steady state. In general, however, they will not be needed, given the rapid arrival at steady state of the DANTE effect (∼1.5 s) relative to the typical duration of a multislice imaging experiment (1–2 min). Finally, we note that distorted gradients would have little effect on the moving spin signal, but could affect the static signal, as phase preservation is a requirement for the static signal. We have pushed the parameters on our scanner by using a DANTE tD of 500 μs and a gradient amplitude 18 mT/m (data not shown) and have seen no apparent static tissue signal loss.
We have described here a new method that uses a train of low FA RF pulses in combination with a blipped field gradient pulse between each RF pulse, repeated regularly, to drive the static tissue into a longitudinal and a transverse steady state. The magnetization of static tissue along the longitudinal direction, therefore, loses very little signal, with the majority of the longitudinal magnetization being preserved for use in image acquisition. Conversely, flowing spins (e.g., blood and CSF), given the same conditions, do not establish a transverse steady state due to quadratic phase accumulation caused by flow along the applied gradient. As a result, the longitudinal magnetization of flowing spins is largely or even fully attenuated. The DANTE-BB preparation technique thus creates a contrast in longitudinal magnetization between the steady state of static spins and the progressive saturation of flowing spins.
The advantages of the approach include: (1) simple incorporation of the DANTE method into existing readout modules, with no additional hardware; (2) high contrast between moving and static spins; (3) a flexible and quantitative capability in controlling flow suppression and achieving static tissue relaxation contrast, via the DANTE FA; (4) a low SAR compared to conventional BB approaches, providing benefit at high magnetic field; and (5) a robust flow suppression effect that is insensitive to flow velocity (above a low threshold).
The authors thank Dr. Jamie Near and Dr. Matthew Robson for their helpful discussions.
To relate Eq.  to the steady-state Eq. , we use the eigenvalue decomposition of A = VΛVT with diagonal matrix Λ containing eigenvalues λi (27):
where the orthogonal eigenvector matrices V result in VTV = VVT = I, and we define:
The magnetization in Eq. [A1] thus consists of two components. The first component decays away from the initial magnetization MI at a rate dictated by the eigenvalues of A. Further, in the limit of n → ∞:
Thus, the second component describes a relaxation toward the standard steady state, independent of the starting magnetization. Unfortunately, the eigenvalues of A are not straightforward to derive in terms of T1, T2, α, etc., for arbitrary values of θ (28). Nevertheless, these expressions can readily be used to calculate the steady state signal behavior for a given A and show essentially perfect agreement with Bloch simulations.