Synopsis

Brain metabolite T₁ and T₂ have diagnostic value and per-subject knowledge of both metabolite and water reference T₁, T₂ is necessary for accurate metabolite absolute quantification. Here we optimize the excitation schedules of our recently-proposed magnetic resonance spectroscopic fingerprinting (MRSF) sequence to accurately estimate metabolite T₁ and T₂. We computationally evaluate the optimized schedules using Monte-Carlo simulations, as well as phantom and in-vivo experiments.

Introduction

Methods

Optimization Variables: We’ve optimized the flip angle of the first pulse (FA), TR and TE for a PRESS-based fingerprinting sequence, for N consecutive excitations. Discrete values for FA= [0:5:150 deg.], TR= [900:10:1600 ms] and TE= [35:5:120 ms] were used. Nine schedule lengths were explored (N=5, 10, 15, 20, 25, 50, 60, 75 and 100), while keeping the SNR per unit time fixed.

Algorithm: Optimization was done using Matlab 2017a’s genetic algorithm toolbox (The Mathworks, Natick, MA). To avoid local minima 2000 starting populations were initialized in four separate optimization runs. Uncoupled singlets were assumed, simulated using the Bloch equations. All spins were driven into dynamic equilibrium.

Target function: A normalized root mean square error, averaged across a range of typical in‑vivo T₁ and T₂ ($$$T1\in{[750-1650]} ms$$$, $$$T2\in{[125-375]} ms$$$), was calculated ($$$\sqrt{bias^2+std^2} = \overline{RMSE} $$$). For simplicity, radiofrequency transmission was assumed homogeneous (B₁₊=1). $$$\overline{RMSE}$$$ was evaluated using Monte-Carlo simulations with 1000 different noise realizations, assuming the SNR from a single 90° excitation of fully relaxed magnetization was SNR_exc=15. To avoid schedules which lead to excessive SNR loss, an additional penalty was added in the form of $$$P=1-(S^{mean}/S^{max}$$$) were $$$S^{mean}$$$ defined as the sum of all excitation in the schedule and $$$S^{max}$$$ defined as the maximal possible signal without any T₁ or T₂ weighting. The target function was $$$\overline{RMSE}+P$$$ .

Schedule evaluation: Once optimized, Monte-Carlo simulations were used to estimate each schedule’s bias (accuracy) and standard deviation (precision) over a range of T₁, T₂ and B₁₊ values found in‑vivo ($$$T1\in{[750-1650]} ms$$$, $$$T2\in{[125-375]} ms$$$ and $$$B_{1+}=1$$$) using SNRexc=10.The sum of the averaged bias and accuracy values was used to assess each schedule’s performance, using a single number.

Phantom experiments: The reproducibility of the optimal schedule was assessed in a 3.375 mL voxel using a homogeneous spherical phantom containing a water solution with metabolites at brain concentrations (NAA: 12.5 mM, T₁/T₂=830/630 ms; Cr: 10 mM, T₁/T₂=600/400 ms; Cho: 2 mM, T₁/T₂=430/340 ms; water T₁/T₂=625/422 ms). The phantom was scanned 18 times and for every 3 scans the phantom was repositioned and reshimmed. Water relaxation was estimated by running the schedule once without water suppression; the resulting non stead state fingerprint was used for water T₁ and T₂ estimation. The total scan time was 6 min. The CVs of NAA, Cr, Cho and water T₁ and T₂ were quantified.

In-vivo experiments: Reproducibility of the optimal schedule was assessed in two volunteers, scanned 10 times each. Spectra were collected from a 4.5 ml voxel placed in parietal white matter (Fig. 4a). Total scan time was fixed at 6 minutes.

Results

Optimization: Figure 1 plots the CV for T₁ and T₂ as a function of schedule length after optimization. The schedule with the optimal CV required only 10 excitations. The optimized FAs, TRs and TEs found are plotted in Figure 2.

Phantom: Phantom reproducibility show CV of 7% and 3% for metabolite and water T₁ estimation (figure 3 left). T₂ CV was 9% and 2% for metabolite and water (figure 3 right).

In-vivo: In-vivo average T₁ CV was 11% and 4% (figure 4b) and T₂ average CV was 11% and 2% (figure 4c) for metabolites and water.

Discussion

Our computer simulations indicate that, for the same total acquisition time, short schedules (with more averages) produce more accurate and precise T₁ and T₂ estimations. Short schedules have other substantial advantages: they are easier to compute, optimize and can be applied to other lengthy acquisitions such as 2D NMR or spectroscopic imaging.

We optimized schedule and schedule length to reduce T₁ and T₂ estimation errors. Optimal schedule was tested in phantom and in-vivo to produce small estimation errors within clinical time scale, as was expected by Monte-Carlo simulations.

Acknowledgements

References

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[2] Kulpanovich A. and Tal A .NMR in Biomedicine 31.11 (2018): e4001;