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Overcoming the Rician Noise Bias of T2* Relaxometry with an Artificial Neural Network (ANN)
Ferdinand Schweser1,2, Thomas Jochmann3, and Robert Zivadinov1,2

1Buffalo Neuroimaging Analysis Center, Department of Neurology, Jacobs School of Medicine and Biomedical Sciences, University at Buffalo, The State University of New York, Buffalo, NY, United States, 2Center for Biomedical Imaging, Clinical and Translational Science Institute, University at Buffalo, The State University of New York, Buffalo, NY, United States, 3Department of Computer Science and Automation, Technische Universit├Ąt Ilmenau, Ilmenau, Germany

Synopsis

Rician noise represents the major source of bias in parametric fitting techniques, such as the estimation of the T2* relaxation time. This bias is particularly strong when the signal-to-noise ratio is low or T2* values are short, such as in clinical cases of severe brain or liver iron overload. In this work, we trained a deep convolutional neural network to recognize Rician noise and compute unbiased relaxation parameters from multi-echo gradient echo data.

Introduction

Noise on MR magnitude images follows a Rician distribution, which means that the noise level and its mean depend on the signal intensity.1 Several studies have demonstrated that Rician noise represents the major source of bias in parametric fitting techniques, such as the estimation of the T2* relaxation time.8-12 This bias is particularly strong when the signal-to-noise ratio is low or T2* values are short, such as in clinical cases of severe brain or liver iron overload.

Several methods have been proposed to address Rician noise bias, such as the Power Method,2,3 echo train truncation,4,5 and the incorporation of an additional offset fitting parameter.6,7 However, these approaches suffer from their own intrinsic biases because they do not model the Rician noise distribution properly.8-12

In this work, we trained an artificial neural network to recognize Rician noise and compute unbiased relaxation parameters from multi-echo gradient echo data.

Methods

Network Architecture: We built an artificial neural network (ANN) with three fully connected hidden layers and rectifying linear unit (ReLU) activation functions in Keras 2.2.0 (12 input nodes, 13*, 12*, and 13* hidden nodes, and two output nodes; * indicates an extra bias node per layer). The model architecture is illustrated in Figure 1.

Training Data Simulation: We used simulated signal decay curves to train the ANN. We simulated mono-exponential decay curves with R2* (=1/T2*) between 0 and 400/s (T2*>2.5ms), maximum signal intensity between 0 and 2 [a.u.], and signal-to-noise ratios (SNRs) between 2 and 40. All parameters were chosen randomly (uniformly distributed) from within the stated intervals. The Rician noise was simulated by adding Gaussian noise to the real and imaginary components of the signal. We mimicked 12 gradient echoes with TE1=4.76ms and ΔTE=3.96ms.

Network training: We trained the network (GPU; NVIDIA GeForce GTX 750 Ti) with the Adam Optimizer (Tensorflow 1.8) using mean squared error loss and data shuffling with 10 million decay curves. We used 100,000 decay curves for the validation.

Conventional methods: For comparison purposes, we applied the following conventional fitting techniques (all logarithmic calculus) to the validation data: direct fitting; fitting of the squared signal after noise correction (“Power Method”); and echo truncation at SNR values below 2, 4, 8, 16, and 32.

MRI: The proposed method was evaluated in vivo using clinical multi-echo gradient echo data acquired at 3 Tesla (same echo times as used for training data generation). Relaxation rate constants were calculated on a voxel-by-voxel basis.

Results

Training and evaluation losses decreased monotonically during the first 4000 epochs and converged to below 1% relative difference. We stopped the training after 6500 epochs.

Figure 2 compares the performance of the proposed method with the conventional methods over the full range of R2* and SNR values in the validation data. The conventional methods substantially underestimated R2* when true values fell below 100/s (T2*<10ms) independent of the SNR (red arrows). The proposed method estimated the true R2* values linearly up to 300/s (T2*>2.8ms). Figure 3 enlarges a randomly chosen subset of samples with R2* values that are typically observed in brain MRI at 3T, which demonstrates underestimation in low SNR regimes even for these moderate relaxation rates.

Figure 4 demonstrates the applicability of the proposed method in the clinical setting and illustrates decreased bias compared to conventional techniques in the iron-laden subcortical gray matter. Furthermore, the comparison revealed that the proposed technique yielded parameter maps with a reduced noise level, probably due to a more appropriate modeling of the underlying noise distribution.

The computation time for the 3D in vivo MRI scan was below 100 seconds on a workstation without GPU (CPU only).

Discussion

The non-linearity of artificial neural networks with non-linear activations allows modeling the Rician noise distribution correctly in the mono-exponential parameter-fitting problem and, hence, substantially extends the range of R2* values that can be obtained reliably with a chosen multi-echo train. The non-linear relationship between quantified and actual R2* values were successfully resolved.

In this work, we used only simulated signal curves for the network training, providing full control over the training process and potential training bias. Depending on the particular sequence parameters, the proposed method will help obtain more reliable estimations of the iron load in the brain and promises to yield more robust clinical estimations of liver iron content in iron overload conditions.

Conclusion

MRI physics-informed artificial neural networks allow the computationally efficient modeling of confounding signal contributions with non-linear underlying relationships, leading to a more accurate quantitation of tissue properties in the clinical setting.

Acknowledgements

Research reported in this publication was funded by the National Center for Advancing Translational Sciences of the National Institutes of Health under Award Number UL1TR001412. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH.

References

1. Gudbjartsson H and Patz S. Magn Reson Med, 34(6):910–914, 1995.

2. Miller AJ and Joseph PM. Magn Reson Imaging, 11(7):1051–6, 1993.

3. Raya JG et al. Magn Reson Med, 63(1):181–93, 2010.

4. Yin X et al. NMR Biomed, 23(10):1127–36, 2010.

5. He T et al. Magn Reson Med, 60(2):350–6, 2008.

6. Du G et al. PLoS One, 7(4):e35397, 2012.

7. Ghugre NR et al. J Magn Reson Imaging, 23(1):9–16, 2006.

8. Beaumont M et al. J Magn Reson Imag, 30(2):313–20, 2009.

9. Feng Y et al. Magn Reson Med, 2013.

10. Marro K et al. Magn Reson Imaging, 29(4):497–506, 2011.

11. Raya JG et al. Magn Reson Med, 63(1):181–93, 2010.

12. Otto R et al. Pediatr Radiol, 41(10):1259–65, 2011.

Figures

Figure 1. Artificial neural network architecture used for parameter fitting in this work. The magnitude signal is fed to the input layer on a voxel-by-voxel basis. The left-most node in the hidden layers denotes the bias to the subsequent layers. The output layer provides the relaxation rate constant, $$$R_2^*$$$, and the extrapolated signal at TE=0ms, $$$S_0$$$.

Figure 2. Comparison of relaxation rate constants computed with the proposed technique and conventional techniques, respectively. The top row compares the computed relaxation rate constants with the ground truth. The straight black line indicates perfect estimation. The middle row shows the percent error of the estimated parameters over the true relaxation rate. The bottom row shows the percentage error over the signal-to-noise ratio. The proposed technique yields considerably improved parameter estimates in the fast relaxation regime (green arrows) compared to conventional techniques that suffer from Rician noise bias (red arrows).

Figure 3. Parameter estimation performance for relaxation rates that are typically observed in clinical brain T2* mapping in patients without iron overload.

Figure 4. Application of the proposed fitting method with logarithmic calculus fitting in the human brain. (a) Relaxation rate constants and extrapolated signal at TE=0ms ($$$S_0$$$) obtained with the proposed technique, logarithmic calculus (middle), and the difference (right). The difference images reveal substantial deviations between the parameter maps in the iron-laden deep gray matter (arrow-top), illustrating Rician noise bias of the conventional approach. The fast decay above the sinus cavity (arrow-bottom) is incorrectly interpreted as $$$S_0$$$ when the conventional technique is used. (b) An enlarged view of the relaxation rate maps illustrating reduced noise level with the proposed technique.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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