Synopsis

An MR fingerprinting (MRF) dictionary can be difficult to generate, especially when the dictionary calculation involves complicated physics. We present a new method, named MRF-GAN, based on the generative adversarial network (GAN) to create MR fingerprints. We demonstrate that MRF-GAN can generate accurate MRF fingerprints and the associated in vivo MRF maps comparing to the conventional MRF dictionary. Moreover, it can significantly reduce the dictionary generation time which opens the door to rapid calculation and optimization of MRF dictionaries with more complex physics.

Introduction

A pre-calculated dictionary is one of the key components of MRF¹. Depending on the tissue property of interest, it can be calculated using different MRF sequences, such as the bSSFP­¹ sequence, the FISP² sequence, or the MRF-X³ sequence. The time required for generating these dictionaries varies, but can be prohibitively long, especially when many factors are included into the calculation. For example, a FISP dictionary requires the simulation of multiple spin evolutions which are then summed for each time frame. Dictionary calculations that involve exchange and other complicated physics can take days to weeks to calculate.

We present a new way to create the MRF dictionaries based on the recent development in unsupervised learning. Specifically, we apply offline the generative adversarial networks (GAN)⁴ to generate MRF fingerprints for given tissue property combinations and sequence parameters. Given the trained MRF-GAN model, this approach can significantly reduce the time needed to generate MRF dictionaries, which makes it possible to generate dictionaries with tissue properties of interest on-the-fly. We believe that this will open the door to the rapid calculation of dictionaries with more complex physics as well.

Methods

GAN is a newly developed unsupervised learning model, which contains two networks: a generative network and a discriminative network. The generative network tries to forge data that mimics the true data; while the discriminative network tries to distinguish the forged data from the true data. They act as two players playing a minimax game and achieve the Nash Equilibrium eventually.

This model is ideal for generating MRF fingerprints. The discriminative network takes training fingerprints and the associated sequence parameters and tissue property combinations to improve its performance in distinguishing real and fake fingerprints. The generative network takes the input of sequence parameters and tissue property combinations of interest, and outputs the fingerprints that mimicking the real ones. We build both networks using 4 layers, with each hidden layer containing 128 neurons and followed by a rectified linear unit. The hyperbolic tangent function and the sigmoid function are used as the activation functions for the output layers of the generative network and the discriminative network respectively. We further modify the GAN so that both networks take control variables, including T1, T2, flip angle, and repetition time. The training data simulated from the Bloch equations contains 1000 time frames and 5970 tissue property combinations with T1 values ranging from 10ms to 2950ms and T2 values ranging from 2ms to 500ms (T1≥T2). A block diagram summarizing the MRF-GAN architecture is shown in Fig.1.

To test our model, an MRF-GAN dictionary is generated using the trained generative network with the same control variables as for the training data, and compared against the training dictionary. We further validate our model using an in vivo brain dataset collected from a healthy volunteer on a Siemens Skyra 3T (Siemens Healthcare, Erlangen, Germany) with the same FISP sequence, a matrix size of 256x256, and a field-of-view of 30cm². T1, T2 maps are created using the MRF-GAN dictionary, and compared to those generated from the MRF-FISP dictionary.

Results

Fig.2 shows several sample fingerprints generated by the proposed MRF-GAN model. Fig.2(a) plots a sample white matter MRF-GAN fingerprint with T1=950ms and T2=40ms. Fig.2(b) shows a sample gray matter fingerprint generated by the MRF-GAN model with T1=1500ms and T2=60ms. Fig.2(c) shows a sample CSF fingerprint generated by the MRF-GAN model with T1=2950ms and T2=500ms. Note that all these MRF-GAN fingerprints match to the MRF-FISP fingerprints well.

The T1 and T2 maps obtained using the MRF-GAN dictionary are shown in Fig.3, column (b). They show no clear visual degradation from the maps obtained from the MRF-FISP dictionary in column (a). The scaled difference maps shown in column (c) further confirm this finding.

Most importantly for the goals here, after the MRF-GAN model is trained, it takes only 7 seconds to generate an MRF dictionary of size 1000x5970. This is a significant reduction in time as opposed to a typical 2-hour generation of an MRF-FISP dictionary.

Discussion and Conclusion

Acknowledgements

References

1. Ma D, Gulani V, Seiberlich N, Liu K, Sunshine JL, Duerk JL, and Griswold MA. Magnetic resonance fingerprinting. Nature 2013, 495:187–192.
2. Jiang Y, Ma D, Seiberlich N, Gulani V, and Griswold MA. MR fingerprinting using fast imaging with steady state precession (FISP) with spiral readout. Magn. Reson. Med. 2015, 74: 1621–1631.
3. Hamilton J, Deshmane A, Griswold MA, and Seiberlich N. MR Fingerprinting with Chemical Exchange (MRF-X) for In Vivo Multi-Compartment Relaxation and Exchange Rate Mapping. Proc. Intl. Soc. Mag. Reson. Med. 24 (2016), 0431.
4. Goodfellow IJ, Pouget-Abadie J, Mirza M, Xu B, Warde-Farley D, Ozair S, Courville A, Bengio Y. Generative Adversarial Networks. arXiv:1406.2661. 2014.