Synopsis

Keywords: MR Fingerprinting/Synthetic MR, Machine Learning/Artificial Intelligence, MRS, Phosporus, Creatine Kinase, MRF

A new magnetization transfer ³¹P Magnetic Resonance Fingerprinting (31P-MRF) technique is emerging to measure the creatine kinase (CK) chemical exchange rate k_CK. The inherent obstacle of the exponential growth in the size of dictionaries with the number of free parameters, was overcome by introducing the nested iteration interpolation method (NIIM). To further reduce the processing time and cope with a nonlinear behaviour, we employed an artificial neuron network (ANN), instead of an interpolation method (IPM) as in the original approach. The nested iteration ANN method (NIAN) is compared with NIIM using simulation data and in vivo ³¹P-MRF data.

Introduction

A new magnetization transfer (MT) phosphorus Magnetic Resonance Fingerprinting (³¹P-MRF) [1] technique is emerging to measure the creatine kinase (CK) chemical exchange rate k_CK, which is key in energy buffering and transport. This framework can largely reduce the scanning time compared to the conventional MT-³¹P spectroscopy methods. The inherent obstacle of the exponential growth in the size of dictionaries with the number of free parameters, was overcome by introducing the nested iteration interpolation method (NIIM) [1]. NIIM showed a great efficiency in both computational and time to estimate 6 free parameters. However, multiple nested iteration paths still need to be computed to perform the linear interpolation. To further reduce the processing time and cope with a nonlinear behaviour, we employed an artificial neural network (ANN), instead of an interpolation method (IPM) as in the original approach. Therefore, this study aims to evaluate the performance of the nested iteration ANN method (NIAN) and compare it with NIIM using simulation data and in vivo ³¹P-MRF data.

Methods

NIIM was recently introduced by Widmaier et al. [1] to overcome the exponential growth of memory and computation time for the generation of dictionaries in the MRF framework [2,3] for high dimensional multi parameter estimations. Like NIIM, the pattern matching process is split into several nested iterations instead of matching all the parameters simultaneously. A schematic framework is shown in Figure 1. The nested iteration is looped N_l=5 times, each time with a different k_CK starting value k_CK ⁰=[0.35,0.2,0.5,0.3,0.4]s^-1. All other parameters in an iterative step are either free (objects of the estimation) or fixed. Parameters are fixed to literature values or estimated values in previous steps. Successively all parameters are estimated. In the last iterative step, all parameters are fixed to estimated values and k_CKⁿ is the objective of the estimation. The other 5 parameters are the longitudinal relaxation rates T₁^ATP,n and T₁^PCr,n, the off resonance f_offⁿ, the B₁ factor f_B1ⁿ and the concentration ratio C_rⁿ=M₀^PCr/M₀^ATP. The 6 estimates in the n^th loop are biased, dependent on the starting value k_CK^0,n. These biased values are then used to find a corrected estimation by either applying the interpolation method (IPM) or an ANN.
The ANN holds four hidden layers (N_in-50-25-15 neurons). Where N_in is the number of input features depending on the number of loops used. A simulated dataset was generated, with 1000 samples with randomly initialized parameters (described above) and added gaussian noise (signal-to-noise-ratio SNR=[0,3,6,9,12,100]dB). It was split into training, validation and test datasets [70/20/10] for simulation validation. Estimations were evaluated for different N_in by choosing the N_l=[1,3,5]. In vivo data acquisition is described in Widmaier et al. [1].
The estimation error was evaluated using the mean absolute percentage error and its standard deviation (STD) for the simulations. In-vivo the test-retest reproducibility was analysed with the coefficient of variance (CV).

Results

Figure 2 shows the comparison of estimation errors for each parameter when applying IPM or ANN in simulated datasets with various SNRs. Additionally, the performance of ANN is evaluated for different numbers of input features. Overall, the ANN shows a more accurate and robust estimation. The number of input features and nested iteration loops have no significant impact on the accuracy.
Table 1 displays mean and standard deviation of estimated parameters from in vivo data over different acquisition times. The estimated values are consistent with those obtained by NIIM and EBIT [4].
The reproducibility is evaluated in figure 3. The CVs of parameters estimated by IPM and ANNs trained under different noise conditions are displayed over the acquisition time. The noise level of the training data does not significantly influence the CVs. The ANN shows a lower CV compared to IPM for all parameters at full acquisition length. For short acquisitions (<9 min) IPM has a lower CV for k_CK.

Discussion and Conclusion

We demonstrate with simulation data, that the NIAN is more accurate and robust in a shorter processing time relative to the NIIM. The exploratory work proved that NIAN needs data just from a single nested iteration path, therefore, processing time and memory can be reduced by 80%. In-vivo human brain data at 7T showed the estimated values are consistent with those reported in the literature and comparable to those obtained with the NIIM and the efficient ³¹P band inversion transfer approach (EBIT) [4]. Overall, the ANN also possesses superior reproducibility on subjects over the IPM through a test-retest experiment. We conclude, that applying NIAN the in the MT-³¹P-MRF pattern matching process is feasible and has great potential in a fast and quantitative measurement of metabolic reactions.

Acknowledgements

This work was supported by the Swiss National Science Foundation (grants n° 320030_189064). We acknowledge access to the facilities and expertise of the CIBM Center for Biomedical Imaging, a Swiss research center of excellence founded and supported by Lausanne University Hospital (CHUV), University of Lausanne (UNIL), Ecole polytechnique fédérale de Lausanne (EPFL), University of Geneva (UNIGE) and Geneva University Hospitals (HUG).”