Synopsis

Keywords: Machine Learning/Artificial Intelligence, Prostate, Relaxometry

This work uses convolutional neural networks (CNNS) with two training strategies for estimating quantitative T2 values from prostate relaxometry measurements, and compares the results to conventional non-linear least squares fitting. The CNN trained with synthetic data in a supervised manner gave lower median errors and better noise robustness than either NLLS fitting or a CNN trained on in vivo data with a self-supervised loss.

Introduction

Quantitative T2 mapping can provide valuable information for prostate cancer diagnosis. Relative to qualitative T2-weighted imaging, quantitative T2 maps give a more objective and potentially sensitive imaging biomarker for diagnosis and grading of prostate cancer (1–3). Mapping is generally performed by acquiring a series of images at multiple echo times, followed by non-linear least squares (NLLS) fitting on a pixel-by-pixel basis to estimate T2 (Figure 1). Prior work from relaxometry (4,5) and similar diffusion applications (6–9) has found that replacing the NLLS fitting with a trained neural network (NN) can greatly speed up processing (6) and reduce the bias associated with least-squares fitting of magnitude images, which have Rician noise (10,11).
One difficulty with these NN approaches is how to perform the training with in vivo data, where the true T2 value is not known. In this work we implement convolutional neural networks (CNNs) trained with two distinct strategies and compare their performance with the conventional NLLS: a self-supervised training strategy, previously described for diffusion problems (6,8), and supervised training using a large synthetic dataset based on the ImageNET database of labelled photographs (12,13), a strategy previously used in image reconstruction (14). We trained CNNs using both strategies and compared their performance with NLLS in synthetic and in vivo datasets. Results showed that both CNNs outperformed NLLS in terms of absolute error, bias, and noise robustness.

Methods

Prostate MRI was acquired on a Siemens 3T Prisma scanner with surface and endorectal receive coils under an IRB-approved protocol. Multi-echo multi-slice fast spin-echo MR images were acquired from 118 participants using the vendor’s spin-echo multi-contrast sequence, with parameters TR=6000 ms, TE=13.2-145.2 ms in 11 increments, 256x256 images with resolution 1.1x1.1 mm, 19-28 slices 3 mm thick. The first echo was discarded to avoid stimulated echo artifacts. Images were split into 86 cases for training and 32 for independent testing.
To generate a synthetic dataset, two sequential images from ImageNET were selected for S0 and T2, scaled (S0 Î[0,1] and T2 Î[0.6.5, 580] ms), and noise was added to create a multi-echo image series with Rician noise following S(TE) = |S0 * exp(-TE/T2) + N(0,σ²) +i N(0,σ²) |, where N(0,σ²) is a Gaussian distribution, with σ sampled from a uniform distribution over [0.001, 0.1]. Ten thousand image series were synthesized for training, and a separate 1,000 series for independent evaluation.
CNNs were based on the enhanced U-Net provided in the MONAI (15) library, with 10 input channels, 4 layers of widths [128, 128, 256, 512], 2 output channels, and 3x3 convolution kernels throughout. The CNN_IMAGENET model was trained in a supervised manner, with a mean squared error (MSE) loss relative to the ground truth S0 and T2. The CNN_SS_INVIVO model was trained using the in vivo training dataset by using the S0 and T2 values output from the network to simulate values of S(TE), and the MSE between simulated and measured data was used as a loss function. Both CNNs were trained in PyTorch (16) for 1000 epochs, batch size=100, AdamW optimizer, LR=0.002. The conventional fitting (FIT_NLLS) used optimize.curve_fit() from Scipy (17) to fit the data to a monoexponential curve to estimate S0 and T2.
Additionally, a noise-addition experiment was performed to evaluate the sensitivity of each method to progressively increasing Rician noise, added artificially to the in vivo evaluation dataset.

Results

Figure 2 gives an example case from the synthetic IMAGENET dataset. In the high-SNR regions the three methods produce similar-appearing results, although CNN_IMAGENET has lower noise. The estimated T2 maps are most different in the low-SNR regions, where the FIT_NLLS show high noise levels, whereas CNN_IMAGENET appears to show blurring.
Figure 3 provides a quantitative comparison of the methods’ performance in estimating T2 maps on the synthetic dataset. In this comparison CNN_IMAGENET has the smallest error and smallest variability of error, and does not show the positive bias (T2pred > T2true) at low SNR seen with FIT_NLLS or CNN_SS_INVIVO.
An example comparing the three methods on an in vivo test case is given in Figure 4. The results appear similar in high SNR regions but differ in lower SNR areas, consistent with the findings on the synthetic test set. The CNN_IMAGENET again shows some evidence of blurring.
Figure 5 shows the impact of increasing noise levels. The noise in the source images propagates into the FIT_NLLS T2 map, but the CNN_IMAGENET map shows consistent results even at high noise levels. As in the synthetic dataset, the CNN_SS_INVIVO method exhibits a modest improvement over FIT_NLLS.

Discussion

The FIT_NLLS and CNN_SS_INVIVO methods showed bias at low SNR levels and sensitivity to increasing noise in the in vivo data, whereas CNN_IMAGENET gave improved accuracy at high noise levels. These results are attributable to CNN_IMAGENET’s ability to correctly model the Rician noise distribution, and the training strategy which provided implicit denoising. Downsides of this synthetic/supervised training strategy include blurring and potential sensitivity to the distribution of T2 values in the training dataset.

Conclusion

We found that a CNN, trained with synthetic data in a supervised manner, gave lower median errors, and better noise robustness than either NLLS fitting or a CNN trained on with a self-supervised loss.

Acknowledgements

This work was sponsored by NIH P41 EB027061, NIH R01 CA241159, NIH S10 OD017974-01

References

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