Synopsis

Brain tissue strain could be a valuable source of information on the brains tissue properties. Therefore, accurate DENSE measurements are crucial, since the computation of tissue strain requires spatial derivatives, which amplifies noise present in the displacement maps. In this work, we optimize the SNR in the displacement maps and substantiate the theory with both computer simulations and measurements. We tested the optimized settings in one volunteer and found a factor of 1.66 SNR increase compared to previously reported experiments. Preliminary results in one volunteer in the basal ganglia showed heartbeat-induced strain of approximately 2.1·10^-3 and inspiration-induced strain of -0.54·10^-3.

Introduction

Theory

For calculating the SNR of the DENSE sequence (Figure 2), we separate the part of the longitudinal magnetization containing tagging information, Q_T (which forms the stimulated echo), from the part of the longitudinal magnetization that has relaxed after the application of the tagging pattern, Q_R. The tagging component of the longitudinal magnetization just before the RF excitation pulse of the k^th­ heart phase image can be written as³$$Q_{T_k}=M_{SS}\mathrm{TAG}(x,y)\exp(-\frac{t_k}{T_1})\exp(-\frac{b_k}{D})\prod_{j=0}^{k-1}\cos(\alpha_j)$$which we adapted to include the diffusion factor. The relaxed magnetization can be recursively written as$$Q_{R_k}=\left(Q_{R_{k-1}}\cos(\alpha_{k-1})-M_0\right)\exp\left(-\frac{(t_k-t_{k-1})}{T_1}\right)+M_0$$In these equations, M_SS is the steady state magnetization just prior to tagging, TAG is the tagging function, t_k is the time of the k^th heart phase after tagging, α_j­ is the flip angle for heart phase j (α₀ is 0, remaining excitation angles were recursively calculated³ to ensure constant signal over heart phases), b_k the effective diffusion weighting at t_k, and T₁ and D the relaxation time and diffusion coefficient of the tissue under consideration, respectively.

The tag spacing T_enc in mm/2π describes the sensitivity of the DENSE sequence and relates to the SNR in the displacement maps by$$SNR_{displ}=\frac{d(t)}{T_{enc}}SNR_{M}$$where SNR_M is the SNR in the magnitude of the stimulated echo image. Large encoding gradients yield an increased displacement sensitivity (smaller T_enc), yet, due to their large b values, reduce the SNR of the magnitude image. Consequently, an optimal T_enc exists for a given apparent diffusion coefficient (ADC) of the tissue. Similarly, a larger final flip angle increases the excited signal, but prevents regrowth of magnetization for the next dynamic. The optimal final flip angle is related to the T₁ of the tissue.

Method

Simulations of the DENSE signal based on the formula’s above were performed in MATLAB for all combinations of T_enc factors (range: 0.1-0.7 mm/2π) and α_max (range: 5-90 degrees). Simulations for a spherical phantom filled with 2% agar gel (T₁: 1700ms, ADC: 1.9·10^-3mm­²/s) were performed, and compared to actual measurements after scaling by a single factor for the unknown noise level in the measurements.

Two phantom measurement series were performed: one for a static T_enc=0.45mm/2π and varying α_max and the other for static α_max=45° and varying T_enc.

Additional validation was performed in one volunteer (male, age 27 years). Written informed consent was obtained in accordance with the Ethical Review Board of our institution. Simulations showed optimal settings of T_enc=0.3mm/2π and α_max=50° (white matter: T₁=1200ms and ADC=0.8·10^-3mm²/s at 7T^4,5). We compared this result with T_enc=0.7mm/2π as was previously used to unravel cardiac and respiratory contributions to brain tissue displacements².

For all validations, we used the cardiac triggered, 2D single-shot DENSE sequence as previously described (Figure 2, Table 1)². A key feature included a time-delay of one cardiac cycle between encoding and decoding to make the sequence more sensitive for respiration induced motion contributions.

Results and Discussion

The SNR_M in the phantom measurements was consistent with computer simulations in both experiments (Figure 3a and 3b). The simulated SNR_displ for both the phantom and white matter is shown in Figure 3c together with the optimal tag spacing.

Imaging was successful in our volunteer; 59 of the 60 dynamics could be used for analysis in both experiments. Consistent strain maps were obtained for both encoding sensitivities (Figure 4). Analysis of the residuals from the linear model² (ROI: Figure 4) showed a reduced standard deviation (T_enc=0.7mm/2π, σ=4.0·10^-3; T_enc=0.3mm/2π, σ=2.4·10^-3, Figure 5), implying an SNR increase of 1.66. In this subject, cardiac-induced brain tissue strain is an order of magnitude larger and in opposite direction compared to the respiration induced strain, despite similar-sized brain translations².

Conclusion

Acknowledgements

References

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