Synopsis

The DW-SSFP sequence is useful to attain strong diffusion-weighting on clinical systems while keeping a short repetition time. However, its analytical model does not account for the echo time. Using a 3D EPG model, we show that the echo time plays an important role, and that it cannot be neglected. We then provide a new method to jointly estimate T₂ and the diffusion tensor on an ex-vivo fetal brain at 3 T.

Introduction

DW-SSFP¹ is a strongly diffusion-weighted sequence with high SNR, high CNR and few artifacts. Although the sequence is conceptually simple, its analytical model² shows that the steady-state signal depends, in addition to the diffusion coefficient, on both T₁ and T₂. This analytical model was developed for a stopped-SSFP spectroscopy experiment and hence does not account for the echo time; it is however still the gold standard when estimating the diffusion tensor from DW-SSFP data³. In this abstract, we use EPG simulations⁴ to explore how the DW-SSFP signal is modified by the TE and to jointly estimate T₂ and the diffusion tensor on an ex-vivo fetal brain.

Methods

We implemented two EPG simulations of the DW-SSFP sequence using the Sycomore toolkit⁵. The first one mimics the analytical model and accounts only for flip angle, diffusion weighting and TR; the second one, more complete, accounts additionally for TE, readout bandwidth, and maximum gradient amplitude. Using reference values of an in-vivo adult human brain at 3 T^6,7 (T₁/T₂ = 1084/69 ms, eigenvalues of D=1708/303/114 µm²/s), and timing parameters achievable on a Siemens 3 T Verio system (flip angle 37°, q=200 cm^-1, TE/TR = 27/30 ms, bandwidth = 1034 Hz/pixel, G_max=25 mT/m, resolution 1 mm isotropic), we compared signals simulated using both EPG models with the analytical model (TE=TR, no bandwidth). We then studied the signal simulated using the complete EPG model on a range of T₂ (100 ms to 400 ms) and D (0 µm²/s to 2000 µm²/s) at two diffusion weightings (q=12 cm^-1 and q=200 cm^-1) and on a range of echo times (5 ms to 25 ms). Finally, on an ex-vivo fetal brain (35 gestational weeks, fixation 22 weeks in 4% formaldehyde followed by 30 weeks in tap water), we acquired DW-SSFP images (60 diffusion-weighted volumes with aforementioned parameters plus 6 additional volumes at q=12cm^-1 and TE 7/12/17/22/27 ms), a XFL-B₁ map⁸, and a VFA-T₁ map⁹. This data was used in an evolutionary algorithm¹⁰ to jointly estimate T₂ and the diffusion tensor; our T₂ estimation was then compared to a bSSFP-T₂ map¹¹.

Results

Figure 1 shows the relative error of the two EPG simulations with respect to the analytical model on a set of 60 directions of the diffusion gradient (i.e. different apparent diffusion coefficients of the same diffusion tensor): the simplified EPG simulation closely matches the analytical model, while the complete model shows that the TE indeed has an effect on the signal, with discrepancies reaching 20 %. Figure 2 shows the signal simulated by the complete EPG model versus the echo time for different values of T₂ (line color) and of D (marker shape): at low diffusion weighting (q=12 cm^-1), the signal depends on T₂ but barely on D while at high diffusion weighting (q=200 cm^-1), the signal depends on T₂, D and TE. On the ex-vivo fetal brain acquisitions, Figure 3 shows the effect of the diffusion weighting on the banding artifacts inherent to SSFP sequences: the artifacts disappear when q is larger than the inverse of the resolution. Figure 4 shows a map of R₂ and a map of the axial diffusivity jointly obtained by our estimation method, and Figure 5 shows a joint histogram of the R₂ values from the bSSFP map and from our method: our method globally underestimates R₂ with respect to the bSSFP map.

Discussion

The TE effect (Figure 1) varies with the ADC and hence cannot be only attributed to T₂ relaxation: for a precise estimation of biophysical parameters, the TE must be accounted for in numerical models of the DW-SSFP. Our EPG model does include this effect, as well as those of the imaging gradients, albeit at the cost of a higher computational load. The removal of the banding artifact through a diffusion weighting dependent on the resolution can be explained by the spoiling effect of the diffusion sensitization gradient. This however implies that artifact-free images at high resolution will require a larger amount of diffusion weighting, thus complicating the T₂ estimation. The lower R₂ estimated by our method may be caused by the finite duration of the RF pulse¹², further experiments are required to validate the correction proposed¹² for SSFP on DW-SSFP. The diffusion tensor estimated by our method also needs to be validated: the aforementioned discrepancy between the analytical model and the EPG simulation, as well as the lack of an obvious equivalence in diffusion weighting between the gold-standard DW-SE and the DW-SSFP are problems that need to be addressed.

Conclusion

We have shown that the analytical model of the DW-SSFP does not fully account for the parameters of the sequence and that the TE has an effect on the observed signal; this limitation can be solved by using an EPG simulation of the sequence. The dependency of the DW-SSFP on T₂ at low diffusion weightings can be exploited in a multi-parametric fit to compute a joint estimation of the T₂ and the diffusion tensor. These results have proven useful in obtaining measures of the diffusion on a ex-vivo fetal brain on a clinical 3 T scanner. The code used in this paper has been published on GitHub¹³.

Acknowledgements

We would like to thank Karla Miller for the DW-SSFP sequence, Cristina Antal for the ex-vivo fetal brain, and the HPC center of the University of Strasbourg for the computing resources.

References

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