Giada Fallo^{1,2}, Matteo Cencini^{2,3}, Pedro A. Gómez^{4}, Davide Bacciu^{1}, Antonio Cisternino^{1}, Michela Tosetti^{2}, and Guido Buonincontri^{2}

Magnetic resonance fingerprinting (MRF) is a useful tool for simultaneously obtaining multiple tissue-specific parameters in an efficient imaging experiment. This technique uses transient state acquisitions with pseudo-random acquisition parameters. However, specific schedules may be better suited for certain parameter ranges or sampling patterns. This work aims to introduce a framework for pulse sequence optimization, including aliasing and noise in our estimates, individually or jointly optimizing for T_{1} and T_{2} relaxation times. We demonstrated the schedules created by our algorithm using MRI acquisitions on a healthy volunteer. The design framework could improve the efficiency and accuracy of T_{1} and T_{2} acquisitions.

Introduction

New methods based on transient-state imaging, including magnetic resonance fingerprintingOur optimisation method was based on a Bayesian optimisation algorithm (BO)^{7,9}. We performed a simulation of an SSFP MRF^{8} signal evolutions with the Extended Phase Graph (EPG) formalism^{12}. To work on a realistic dataset, we used the 100^{th} slice of a numerical phantom brain from the Brainweb database^{11}, where we also included under-sampling artefacts by applying forward and backward non-uniform Fourier transform^{13} for each frame. Complex white Gaussian noise was added to the raw k-space data. The overall errors of the quantitative maps was used as the cost function (l2 norm of the difference between maps), excluding the background values. We first individually optimised T_{1} and T_{2} estimations; then, we optimised for the two parameters simultaneously. In the latter case, we used the sum of the overall errors of T_{1} and T_{2} maps as a cost function. We considered three ways of generating the function consisting of *m* excitations for FA or TR sequences, where the schedule length *m* was one of the input parameters of our optimisation model:

- FFT method: We used the first coefficients of a Fourier series, zero-padding the remaining to estimate a slow-varying function.
- Perlin method: To produce Perlin noise we generated normally distributed random numbers and interpolated them with a cosine function.
- Combined method: We also used the combination of the two methods described before, using Perlin noise for TR and Fourier coefficients for FA.

The optimised schedules were evaluated in vivo on the brain of a volunteer, using a GE *Hdxt 1.5T* scanner equipped with an *8ch* receive coil (Milwakee, US).

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Figure 1. Optimised schedules obtained with the three methods optimizing T_{1} and T_{2} individually and jointly (in order, from top to bottom: FFT, Perlin and Combined method).

Figure 2. Parametric maps of simulated experiments obtained from the benchmark scheme and from two of the optimised schedules, Perlin T_{1 }and Combined T_{1}-T_{2}. (a) Reconstructed T_{1} maps and associated relative error maps. (b) Reconstructed T_{2} maps and associated relative error maps.

Figure 3. Overall errors computed for parametric maps of simulated experiments, obtained from the benchmark and the optimized schedules. In blue, overall error of the T_{1} reconstruction for each scheme. In orange, overall error of the T_{2} reconstruction for each scheme. Overall errors where the smallest with the combined T_{1}-T_{2 }optimization.

Figure 4. Parametric maps of in-vivo experiments using the benchmark scheme, Perlin T_{1} and Combined T_{1}-T_{2}. (a) Reconstructed T_{1 }maps and associated relative error maps. (b) Reconstructed T_{2 }maps and associated relative error maps

Figure 5. Errors computed on white matter region for parametric maps of in-vivo experiments, obtained from the benchmark and the optimized schedules. In blue, overall error of the T_{1 }reconstruction for each scheme. In orange, overall error of the T_{2} reconstruction for each scheme.