Elad Rotman^{1}, Onur Afacan^{2}, Sila Kurugol^{2}, Simon K Warfield^{2}, and Moti Freiman^{1}

^{1}Faculty of Biomedical Engineering, Technion-IIT, Haifa, Israel, ^{2}Computational Radiology lab, Boston Childrenâ€™s Hospital, Harvard Medical School, Boston, MA, United States

Recently, unsupervised deep-learning showed improved performance in estimating the “Intra-Voxel incoherent motion” (IVIM) signal decay model parameters from Diffusion-weighted Magnetic Resonance Imaging (DW-MRI) data compared to classical methods. However, such deep-learning models do not generalize well on acquisitions with a high signal to noise ratio (SNR). In this work, we introduce SUPER-IVIM-DC, a supervised deep learning network coupled with a data consistency term to improve the capacity of deep-learning-based models to generalize the IVIM signal decay model. We demonstrated an improvement in model generalization, accuracy, and homogeneity using simulation, phantom, and in-vivo experiments.

$$\underbrace{\underbrace{\alpha_{D^*}\sum(D^*-\hat{D^*}) + \alpha_{D}\sum(D-\hat{D}) + \alpha_{f}\sum(f-\hat{f})}_{Supervised \ loss} + \alpha_{Recon}\underbrace{\sum(F(\theta)-F(\hat{\theta}))}_{Reconstruction \ loss}}_{SUPER-IVIM-DC \ loss}$$

We followed the IVIM-NET training approach to train SUPER-IVIM-DC. We evaluated the networks using three experiments. First, we tested the noise response of the networks on computer-generated simulation data. We use the same b-values as used in the IVIM-NET for training [8]. For evaluation, 5000 samples were used as an input for the networks. The input data was correlated to the network’s SNR. We used the normalized root-mean-squared error (NRMSE) as the evaluation metric. Second, we tested the bi-exponential fitting performance of the networks using a phantom. The phantom was comprised of 6 small vials of different liquid substances [9], [10]. We scanned the phantom using a 9.4T/20 Animal MRI scanner (Bruker Biospec, Ettlingen, Germany) with the following b-values: {100, 300, 500, 700, 900, 1100, 1300, 1500, 1900, 2100, 2300, 2500} and retrained the networks with this set of b-values. We selected a region-of-interest (ROI) from a relatively homogeneous area in each of the six vials and used it as an input for the DNN. The IVIM parameters were evaluated and assigned in the IVIM equation to create an IVIM curve estimation and coefficient of variance (CV) of every ROI calculated. Last, we tested the networks' homogeneity estimations on 9 clinical DW-MRI studies [11]. The in-vivo abdominal imaging was performed using a 1.5 [T] (Magnetom Avanto, Siemens Medical Solutions, Erlangen, Germany) with the following b-values: {0, 50,100,200, 400,600,800}. A single slice containing the kidneys, spleen, and liver was selected. A homogenous ROI was marked on every organ and used as input. Statistical analysis was performed on every ROI for each IVIM parameter estimation.

Our phantom study shows that SUPER-IVIM-DC reduced the CV mean value compared to IVIM-NET for D* and f. Specifically, for the 9% dairy cream vial, SUPER-IVIM-DC reduced the CV mean value in D* by 52% (0.02 vs. 0.04), for f by 92% (0.009 vs. 0.115), and with similar results on D (0.033 vs 0.031).

Figure 3 depicts the IVIM parametric maps estimated from clinical abdominal DW-MRI data by SUPER-IVIM-DC (bottom row) and by IVIM-NET (top row). SUPER-IVIM-DC reduced the CV median value compared to IVIM-NET. The major difference was measured on the spleen. SUPER-IVIM-DC reduced the D* CV median value by 73% compared to the IVIM-NET (0.05 vs 0.198 p<1e-4).

[1] D. M. Koh, D. J. Collins, and M. R. Orton, “Intravoxel incoherent motion in body diffusion-weighted MRI: Reality and challenges,” Am. J. Roentgenol., vol. 196, no. 6, pp. 1351–1361, 2011, doi: 10.2214/AJR.10.5515.

[2] L. M. Le Bihan, Breton E, Lallemand D, Aubin ML, Vignaud J, “Separation of diffusion and perfusion in intravoxel incoherent motion MR imagingSeparation of diffusion and perfusion in intravoxel incoherent motion MR imaging,” in RSNA, 1988, vol. 1, no. 2, pp. 12–17.

[3] D. M. Koh and D. J. Collins, “Diffusion-weighted MRI in the body: Applications and challenges in oncology,” Am. J. Roentgenol., vol. 188, no. 6, pp. 1622–1635, 2007, doi: 10.2214/AJR.06.1403.

[4] J. Patel, E. E. Sigmund, H. Rusinek, M. Oei, J. S. Babb, and B. Taouli, “Diagnosis of cirrhosis with intravoxel incoherent motion diffusion MRI and dynamic contrast-enhanced MRI alone and in combination: Preliminary experience,” J. Magn. Reson. Imaging, vol. 31, no. 3, pp. 589–600, 2010, doi: 10.1002/jmri.22081.

[5] M. Freiman et al., “Characterization of fast and slow diffusion from diffusion-weighted MRI of pediatric Crohn’s disease,” J. Magn. Reson. Imaging, vol. 37, no. 1, pp. 156–163, 2013, doi: 10.1002/jmri.23781.

[6] M. C. Zhang et al., “IVIM with fractional perfusion as a novel biomarker for detecting and grading intestinal fibrosis in Crohn’s disease,” Eur. Radiol., vol. 29, no. 6, pp. 3069–3078, 2019, doi: 10.1007/s00330-018-5848-6.

[7] S. Barbieri, O. J. Gurney-Champion, R. Klaassen, and H. C. Thoeny, “Deep learning how to fit an intravoxel incoherent motion model to diffusion-weighted MRI,” Magn. Reson. Med., vol. 83, no. 1, pp. 312–321, 2020, doi: 10.1002/mrm.27910.

[8] M. P. T. Kaandorp et al., “Improved unsupervised physics-informed deep learning for intravoxel incoherent motion modeling and evaluation in pancreatic cancer patients,” Magn. Reson. Med., vol. 86, no. 4, pp. 2250–2265, 2021, doi: 10.1002/mrm.28852.

[9] Z. Ababneh, M. Haque, S. E. Maier, and R. V. Mulkern, “Dairy cream as a phantom material for biexponential diffusion decay,” Magn. Reson. Mater. Physics, Biol. Med., vol. 17, no. 2, pp. 95–100, 2004, doi: 10.1007/s10334-004-0063-7.

[10] G. S. Ioannidis, K. Nikiforaki, G. Kalaitzakis, A. Karantanas, K. Marias, and T. G. Maris, “Inverse Laplace transform and multiexponential fitting analysis of T2 relaxometry data: a phantom study with aqueous and fat containing samples,” Eur. Radiol. Exp., vol. 4, no. 1, 2020, doi: 10.1186/s41747-020-00154-5.

[11] V. Taimouri et al., “Spatially constrained incoherent motion method improves diffusion-weighted MRI signal decay analysis in the liver and spleen,” Med. Phys., vol. 42, no. 4, pp. 1895–1903, 2015, doi: 10.1118/1.4915495.

Schematic illustration of SUPER-IVIM-DC network:
dark blue represents the supervised loss and light blue represents the unsupervised
loss.

The normalized root-mean-squared-error of IVIM
parameter predictions comparison between the 11 b-values trained networks.
(Left) the diffusion coefficient (D), (Middle) pseudo-diffusion coefficient(D*)
(Right) pseudo-diffusion fraction (f)

IVIM parameter
maps estimated using IVIM-NET (Top) SUPER-IVIM-DC (bottom)

DOI: https://doi.org/10.58530/2022/2531