3D Cartesian fast interrupted steady‐state (FISS) imaging

Purpose To enable intrinsic and efficient fat suppression in 3D Cartesian fast interrupted steady‐state (FISS) acquisitions. Methods A periodic interruption of the balanced steady‐state free precession (bSSFP) readout train (FISS) has been previously proposed for 2D radial imaging. FISS modulates the bSSFP frequency response pattern in terms of shape, width and location of stop band (attenuated transverse magnetization). Depending on the FISS interruption rate, the stop band characteristic can be exploited to suppress the fat spectrum at 3.5 ppm, thus yielding intrinsic fat suppression. For conventional 2D Cartesian sampling, ghosting/aliasing artifacts along phase‐encoding direction have been reported. In this work, we propose to extend FISS to 3D Cartesian imaging and report countermeasures for the previously observed ghosting/aliasing artifacts. Key parameters (dummy prepulses, spatial resolution, and interruption rate) are investigated to optimize fat suppression and image quality. FISS behavior is examined using extended phase graph simulations to recommend parametrizations which are validated in phantom and in vivo measurements on a 1.5T MRI scanner for 3 applications: upper thigh angiography, abdominal imaging, and free‐running 5D CINE. Results Using optimized parameters, 3D Cartesian FISS provides homogeneous and consistent fat suppression for all 3 applications. In upper thigh angiography, vessel structures can be recovered in FISS that are obscured in bSSFP. Fat suppression in free‐running cardiac CINE resulted in less fat‐related motion aliasing and yielded better image quality. Conclusion 3D Cartesian FISS is feasible and offers homogeneous intrinsic fat suppression for selected imaging parameters without the need for dedicated preparation pulses, making it a promising candidate for free‐running fat‐suppressed imaging.


Double Echo in Steady State (DESS)
We present the CRLB optimization of this sequence in the Supplementary Information to show the flexibility of our method.
Double-Echo in Steady State (DESS) has been used to quickly acquire high resolution T2 maps in the knee (Chaudhari, 2018). DESS captures two images with different contrasts by acquiring two echos in a single TR. The two echos are separated by a spoiler gradient. The first image S1 has an effective echo time of TE, while the second image S2 has an effective echo time of 2TR -TE. The S2 image has reduced SNR due to additional T2 decay and because the primary signal contribution is from magnetization that was rephased after the second RF pulse. The T2 can be estimated from the ratio image S2/S1 if the T1 of the tissue is known using Eq. 7 from Sveinsson et al. (Sveinsson, 2017).
The derivative of the CRLB loss with respect to sequence parameters ( , TR) was also computed using backpropagation. One hundred TRs were used to reach steady-state. The optimization was performed for 10 different initializations over the grid alpha=[10:10:50], TR = [25,35] with 10 EPG states.
The phantom was scanned at 3T (GE Signa Premier) with scan parameters determined by the CRLB optimization (alpha, TR) and the following acquisition parameters: FOV = 22.5 x 22.5 cm, matrix size = 416 x 416 x 176, in-plane resolution 0.54 x 0.54 mm, slice thickness 1 mm, 48-channel head coil, BW = +/-31.25 kHz, 2 x 2 ARC undersampling. T1 values for the DESS calculation were obtained using Inversion-Recovery T1 mapping. The standard deviation of the T2 estimates from the two acquisitions were compared to show the effect of the CRLB optimization in different species.
Supporting Information for "Flexible and Efficient Optimization of Quantitative Sequences using Automatic Differentiation of Bloch Simulations" (Lee et al.) Figure S2: Left: The overall structure of the DESS graph is the same as the DESPOT1 graph shown above. Only one forward Bloch simulation is necessary. The 'bloch_operator' block computes relaxation and RF matrices that can be reused between TRs to reduce the total number of nodes in the graph. Right: A single TR Bloch in the DESS simulation. This block has an additional relaxation operation and different ordering compared to DESPOT1 since two echos are acquired in a single TR.

Supporting Information
The sequence parameters obtained for the cartilage-like species were alpha = 33 degrees and TR = 32.5 ms. For the meniscus-like species, the parameters were alpha = 45 degrees and TR = 21 ms (minimum). Optimization over 10 different initializations took 357 seconds per tissue on a single CPU. We observed that the solution did not depend on the initialization.
For the sequence targeting the longer T2 species, the TR was lengthened to 32.5 ms to increase the second effective echo time to (2TR -TE) = 58.5 ms. Flip angle differences between the two species take advantage of differing T1 relaxation. The acquisition time was 7:55 minutes for the scan parameters targeting the cartilage-like species, and 5:06 minutes for the meniscus-like species.
The results from the two phantom scans are shown in SI Figure 3. For the cartilage-like species (T2-8), the T2 distribution is Gaussian. For the meniscus-like species (T2-12), the T2 distribution is Rician due to low SNR in the magnitude images.
For vial T2-8, the cartilage-optimized scan improved the T2 standard deviation in the cartilage-like species from 13.4 to 4.9 ms when compared to the meniscus-optimized scan. For vial T2-12, the T2 standard deviation in the meniscus-like species was 0.4 ms when using the meniscus-optimized scan. The T2 estimation for meniscus in the cartilage-optimized scan exhibited considerable mean bias shift. This is caused by low SNR in the meniscus due to T2 decay at the second effective echo time which results in Rician noise bias. The variance was further amplified by Gibbs ringing in the S2 images, which caused T2 estimates larger than 30 ms.

Supporting Information for "Flexible and Efficient Optimization of Quantitative Sequences using Automatic Differentiation of Bloch Simulations" (Lee et al.)
5 This result demonstrates that the assumption of high SNR made in the ratio distribution approximation must be held for the CRLB optimization to be accurate. Although the cartilage-optimized scan would not be used in practice due to prolonged scan times, poor T2 estimation in the meniscus, and overall reduced SNR efficiency, it demonstrates that the sequence parameters generated with CRLB optimization with automatic differentiation can effectively target different tissues. Using automatic differentiation to optimize the coefficient of variation between the meniscus and cartilage would produce sequence parameters that have more consistent T2 error in each tissue. Figure S3: A slice from the ISMRM/NIST T2 phantom is shown. The S2 images have different contrast when compared to the S1 images due to the longer second effective echo time.

Supporting Information
The histograms for the T2 values estimated in the cartilage-like and meniscus-like vials (indicated by arrows), with the true T2 values denoted by the vertical line, are shown. For the cartilage-like vial, the variance in the cartilage-optimized scan (blue) is reduced compared to the meniscus-optimized scan. For the meniscus-like species, the T2 values (orange) exhibit mean shift and increased variance in the cartilage-optimized scan due to low SNR and Gibbs ringing in the second echo.
Supporting Information for "Flexible and Efficient Optimization of Quantitative Sequences using Automatic Differentiation of Bloch Simulations" (Lee et al.) 6

Magnetic Resonance Fingerprinting (MRF)
Supporting Information Figure S4: A sample TensorFlow graph for MRF using 10 TRs is shown. This graph demonstrates the quadratic runtime scaling when computing the CRLB using reverse differentiation. For this reason, autograd was used to compute the CRLB for MRF with forward differentiation.

Using Autograd for Non-EPG Bloch Simulations
In this section, we apply automatic differentiation to reproduce one of the optimizations in Reeth et al. (2018). We design a prep pulse with 3 discrete flip angles, and 3 discrete TRs to maximize the contrast between two tissues corresponding to the experiment in Reeth Section 2.7. The gradient of the objective (the contrast) with respect to the control variables (alphas, TRs) is calculated using automatic differentiation. This allows us to perform this optimization without using finite differences. The contrast is calculated for 100 off-resonance values ranging from -500 Hz to 500 Hz, which can easily be simulated. We used the SLSQP implementation with the number of iterations capped to 100.
The optimization converged in 100 iterations, with the optimal answer being: flip angles (90, 180, 90), and TRs (14, 14, 677) ms. This is similar to the optimal solution obtained by Reeth et al. with small discrepancies in the repetition time due to differences in beta.
Interestingly, the optimization converges to a 'spin echo' solution (180 degree refocusing pulse with equal spacing on either side) which is well known to be robust against off-resonance.

Fisher Information at Different Iterations of MRF CRLB Optimization
Supporting Information Figure S5: Top: The Fisher Information (FIM) at each echo for different iterations is shown. Although the CRLB depends on the orthogonality of the FIM due to the matrix inversion, a scalar increase in the FIM at each echo will improve (reduce) the CRLB. An interesting observation is that the T2 FIM in the optimal solution is very small between TRs 50 and 150, implying that early echos have very little T2 contrast. Bottom: The mean squared T1 and T2 FIM at each iteration of the optimization is shown. The T1 FIM is reduced by a small amount, while the T2 FIM approximately doubled. This is reflective of the improvement in the relative T1 and T2 CRLB components shown in the main manuscript.

Flip Angle and TR Convergence for MRF CRLB SLSQP Optimization
Supporting Information Figure S6: Convergence progression of the SLSQP optimization at different iterations for MRF IR-FISP with 400 TRs (left) and 1000 TRs (right). For the 1000 TR case, the TRs converge at around iteration 100 and cease to update after they have converged. This suggests that a greedy optimization approach may achieve a reasonable solution. A greedy heuristic would lock variables that have converged at the bounds set by the constraint after a minimum number of iterations, reducing the step update time which would improve runtimes for large numbers of parameters. For the 1000 TR case, the optimization took roughly 16 CPU hours for 350 iterations.

Sensitivity of the CRLB Optimized Sequence to B1 and Off-Resonance
To evaluate the bias sensitivity of the CRLB sequence to confounding factors in vivo, we performed a simulated dictionary matching experiment for the CRLB optimized and initialization schedules. An ideal dictionary assuming B1 = 1.0 and on-resonant (df = 0) was generated for tissues T1 = [1200:3:1500], T2 = [50:1:120] ms. We matched a noiseless fingerprint with T1/T2 = 1330/80 ms to this dictionary for B1 values of 0.8 to 1.2, and off-resonance values ranging from -40 Hz to 40 Hz. The results are shown in Figure S7. The estimated T1 and T2 of the conventional sequence is insensitive to off-resonance. The CRLB optimized sequence T2 estimate becomes shorter and the T1 estimate becomes longer as the offresonance increases. The simulation also indicates that the CRLB optimized sequence has increased sensitivity to B1.
Dictionary matching is unbiased assuming that the model is ideal. Unmodelled phenomena skews the parameter match to certain T1/T2 values. As an extreme case, suppose that a strong water fingerprint was erroneously added to each pixel in the time series. If unaccounted for in the dictionary, the dictionary match would result in all voxels being water. This is the principle used in multicomponent fingerprint matching, where multiple T1/T2 fingerprints are identified per voxel (McGivney, 2018) and the strongest T1/T2 fingerprint shows the strongest cluster.
The bias from this simulation does not exactly match the bias that is observed in vivo but demonstrates how confounding factors can have a greater effect on the CRLB optimized sequence. In vivo, we observe a longer T2 and a longer T1 when using the CRLB optimized sequence. This simulation matches the bias trend that exists in MRF phantom experiments shown in Figure S8.
In Figure S8, we performed ten consecutive undersampled MRF acquisitions of the ISMRM NIST T2 phantom for each of the 1000 TR CRLB optimized and conventional sequence, using the schedule shown in Figure S6. The reference values are published T1/T2 values for the phantom obtained using NMR (Keenan, ISMRM 2016, Program #3290). The scan was done at 3T using an 8-channel head coil and each scan was approximately 14 seconds. The FOV was 22.5 cm, with a matrix size of 192 x 192. The magnetization was allowed to fully recover to equilibrium between acquisitions. Calculating the mean T1 and T2 in each sample ROI allows us to quantify the bias, and the normalized standard deviation across separate acquisitions demonstrates the improvement of the CRLB optimized sequence against white noise. The normalized standard deviation was computed for each voxel in the phantom by calculating the standard deviation of the T1/T2 estimate in the acquisitions dimension and dividing by the mean T1/T2 estimate of that voxel. Figure S8 shows that the CRLB sequence has improved performance against white noise and that bias in the T1/T2 estimate exists after changing the sequence parameters.
We also acquired three different slices from the brain of a consenting volunteer under IRB approval using a 1000 TR conventional and CRLB optimized sequence. The scan was performed using undersampled spirals and reconstructed using dictionary matching. T2 maps from the acquisition are shown in Figure S9 and demonstrate that the in vivo T2 bias trend observed in the fully sampled scan also exists in the undersampled scans. Figure S7: Top: The result of the imperfect fingerprint matched to the ideal dictionary demonstrates greater sensitivity of the CRLB optimized fingerprint to off-resonance and B1 effects. The conventional schedule has little sensitivity to off-resonance. The true value of the tissue of T1/T2 = 1330/80 ms is marked as the dashed black line. The on-resonance, no B1 variation simulation is marked with a circle and shows no bias. Bottom: Conventional and CRLB optimized fingerprints for different values of off-resonance. In the conventional sequence, there is no visible deviation of the fingerprint. In the CRLB optimized sequence, deviations are apparent at TR index 200 and 350. Figure S8: Left: Mean parameter estimates obtained in the ISMRM NIST T2 phantom are compared for the CRLB optimized (red) and conventional (blue) MRF schedules. Reference T1 and T2 values on the x-axis are published parameter values obtained from NMR. The CRLB Optimized schedule overestimates T1 across the range of sample values relative to the conventional schedule. The T2 estimate from the CRLB optimized schedule is marginally underestimated compared to the conventional schedule for the 100 -200ms range, which is opposite to what is observed in vivo. Right: The mean normalized standard deviation across each sample for the repeated undersampled acquisition is shown. Similar to the fully sampled in vivo measurements, the performance of the T1 estimate is unchanged. The error in the T2 estimate is improved across the samples, but the magnitude of the improvement is reduced compared to the fully sampled in vivo case. This may be due to increased offresonance in the ISMRM NIST phantom, since the samples are small and have a plastic shell to separate it from water.