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SARDU-Net: a new method for model-free, data-driven experiment design in quantitative MRI

Francesco Grussu^1,2, Stefano B. Blumberg², Marco Battiston¹, Andrada Ianuș³, Saurabh Singh⁴, Fiona Gong⁴, Hayley Whitaker⁴, David Atkinson⁴, Claudia A. M. Gandini Wheeler-Kingshott^1,5,6, Shonit Punwani⁴, Eleftheria Panagiotaki², Thomy Mertzanidou², and Daniel C. Alexander²
¹Queen Square MS Centre, Queen Square Institute of Neurology, Faculty of Brain Sciences, University College London, London, United Kingdom, ²Centre for Medical Image Computing, Department of Computer Science, University College London, London, United Kingdom, ³Champalimaud Research, Champalimaud Centre for the Unknown, Lisbon, Portugal, ⁴Centre for Medical Imaging, University College London, London, United Kingdom, ⁵Department of Brain and Behavioural Sciences, University of Pavia, Pavia, Italy, ⁶Brain MRI 3T Center, IRCCS Mondino Foundation, Pavia, Italy

Synopsis

This work introduces the “Select and retrieve via direct up-sampling” network (SARDU-Net), a new method for model-free, data-driven quantitative MRI (qMRI) experiment design. SARDU-Net identifies informative measurements within lengthy acquisitions and reconstructs fully-sampled signals from a sub-protocol, without prior information on the MRI contrast. It combines two deep networks: a selector, which selects a signal sub-sample, and a predictor, which retrieves input signals. SARDU-Net can be run with standard computational resources and can increase the clinical appeal of qMRI. Here we demonstrate its potential on qMRI of prostate and spinal cord, two areas where fast acquisitions are key.

Introduction

The latest quantitative MRI (qMRI) acquisitions have increased dramatically the number of images¹ and contrasts² that can be acquired per unit time. However, the increased acquisition complexity makes the design of clinically viable protocols challenging. Clinical acquisitions need to capture salient characteristics of vast sampling spaces within acceptable times, trading off between scan duration and protocol richness³.

Here we tackle the issue of designing compact samplings in vast acquisition spaces by introducing the “Select and Retrieve via Direct Up-sampling” network (SARDU-Net), which identifies informative measurements within lengthy qMRI acquisitions. Unlike state-of-the-art statistical methods as those based on Fisher information⁴, SARDU-Net does not rely on any explicit signal model/representation^5,6. We demonstrate its potential on data from prostate and spinal cord, two areas difficult to image due to physiological noise^7,8, for which rapid acquisitions are imperative.

Methods

Algorithm
We implemented SARDU-Net in PyTorch using two fully-connected deep neural networks (DNNs) (Figure 1). The first DNN is a selector, taking as input a measured voxel signal s and selecting a sub-set w⨂s, where weights w nullify non-relevant measurements. The second DNN is a predictor, outputting u, an estimate of s obtained from w⨂s. The two DNNs are optimised jointly end-to-end⁹ by minimising $$$L = ||\bf u - \bf s||_2^2$$$, so that the selected sub-set is the one enabling the best reconstruction of the input signals.

Acquisition
Prostate We studied scans from 7 men referred for prostate MRI following suspicion of cancer within the INNOVATE trial¹⁰. We focussed on diffusion-weighting imaging (DWI) (VERDICT¹¹ protocol: b={0, 90, 500, 1500, 2000, 3000} s/mm²; resolution: 1.25×1.25×5 mm³) and multi-echo luminal water imaging¹² (LWI) (32 echoes; TE_min/echo spacing: 31.25/31.25 ms/ms; resolution: 0.94×0.94×4.4 mm³), acquired on a 3T Philips Achieva.

Spinal cord We studied spinal cord ZOOM-EPI¹³ scans acquired on 4 healthy volunteers (2 males, scan-rescan) with a 3T Philips Achieva (resolution: 1×1×5 mm³), consisting of 98 measurements: 68 DWIs¹⁴ (b={0, 300, 1000, 2000, 2800} s/mm²); 10 inversion recovery images¹⁵ (inversion times in [100; 2300] ms); 11 magnetisation transfer images¹⁵ (11 off-resonance saturations); 7 multiple-TE images (mTE, TE={25, 40, 55, 70, 85, 100, 200} ms).

Post-processing
Prostate DWI was co-registered non-linearly to LWI using NiftyReg¹⁶, where a prostate mask was segmented manually. Concatenating 10 DWIs-32 LWIs provided 42 measurements.

Spinal cord We corrected data for motion and segmented the cord with SCT¹⁷.

Training
For both data sets we used SARDU-Net to select informative sub-protocols. As a test case we searched sub-protocols that are 50% (half) and 33% (a third) of the original length, although end users could search for any length.
We trained SARDU-Net for 1000 epochs using 80%-20% of prostate/cord voxels as training-validation sets (4 hidden layers for selector/predictor; learning rates: 0.001/0.0001 for 50%-33% task). We adopted a leave-one-out strategy, training in turn a SARDU-Net on all subjects but one, left out for testing.

Analysis
We tested whether SARDU-Net selects sub-protocols that capture salient characteristics of input signals. Firstly, we evaluated popular metrics from SARDU-Net signal reconstructions, namely: apparent diffusion coefficient (ADC), kurtosis (K), luminal water fraction (LWF) (prostate); fractional anisotropy (FA), T1, T2, magnetisation transfer ratio (MTR) (spinal cord). Afterwards, we compared those metrics to their counterparts obtained from the original data by bootstrapping median errors across subjects (i.e. median(m_SARDU – m_TRUE), with m representing a metric; 1000 bootstraps).

Results

Prostate imaging
Figure 2 shows sub-protocol selections in two leave-one-out folds. SARDU-Net selects low/intermediate b-values (DWI) and TE up to about 500 ms (LWI). Results are consistent across folds. Training takes ~1sec per epoch on a 8-core, 2.7 GHz Intel Core i7 processor.

Figure 3 shows SARDU-Net image reconstructions and quantitative metrics. Reconstructed images resemble the acquired data on visual inspection and support accurate model fitting. We do not detect significant biases in reconstructed ADC, K, LWF (error confidence intervals contain error=0).

Spinal cord imaging
Figure 4 shows sub-protocol selections in two leave-one-out folds. SARDU-Net sub-samples heavily DWI, the longest scan, and selects measurements from all of MT, IR, mTE. Computational time per epoch is comparable to the prostate data.

Figure 5 shows SARDU-Net reconstructions and quantitative metrics. There is good correspondence between predicted and acquired data. We do not detect significant biases in FA, T1, T2, MTR (error confidence intervals contain error=0), although fine-scale anatomical details are blurred as sub-sampling gets stronger.

Discussion

In this work we introduce SARDU-Net, a deep learning tool for model-free, data-driven qMRI experiment design. SARDU-net detects informative measurements within vast acquisition spaces where brute-force searches are intractable. It does not rely on any prior MRI signal model, and can be run on commonly available resources.

SARDU-Net can be trained on both simulated and in vivo data, and is ideally placed to guide the design of large clinical studies from a small number of test scans. Here we demonstrate it by selecting informative sub-protocols within lengthy prostate and spinal cord qMRI, shortening scan time with minimal information losses.

Conclusion

SARDU-Net gives new opportunity to identify economical but informative data sets for clinical applications under high time pressure. Using a small number of rich acquisitions from a pilot study with long acquisition times, it identifies the most informative sub-protocol given a specific time constraint.

Acknowledgements

This project has received funding under the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 634541 and 666992, and from: Engineering and Physical Sciences Research Council (EPSRC EP/R006032/1, M020533/1, G007748, I027084, N018702); Prostate Cancer UK Targeted Call 2014: Translational Research St.2, project reference PG14-018-TR2; Spinal Research (UK), Wings for Life (Austria), Craig H. Neilsen Foundation (USA) (jointly funding the INSPIRED study); Wings for Life (#169111); UK Multiple Sclerosis Society (grants 892/08 and 77/2017); the Department of Health's National Institute for Health Research (NIHR) Biomedical Research Centres and UCLH NIHR Biomedical Research Centre; Champalimaud Centre for the Unknown, Lisbon (Portugal). We thank Philips Healthcare for assistance in protocol development and for access to research protocols.

References

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7. Haider MA, Yao X, Finelli A et al. Multiparametric magnetic resonance imaging in the diagnosis of prostate cancer: a systematic review. Clinical Oncology 2016; 28(9): 550-567.

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10. Johnston E, Pye E, Bonet-Carne E et al. INNOVATE: A prospective cohort study combining serum and urinary biomarkers with novel diffusion-weighted magnetic resonance imaging for the prediction and characterization of prostate cancer. BMC Cancer 2016; 16(1): 816-826.

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Figures

Figure 1: architecture of SARDU-Net, made of two fully-connected deep neural networks (DNNs, cascades of linear, ReLU and dropout layers). The first DNN is a selector, which takes as input an MRI signal and outputs a set of weights that nullify non-salient measurements. It contains a soft-min layer and a thresholding stage that zeroes the least-firing output neurons. The second DNN is a predictor, which retrieves the fully-sampled signal from the sub-set received from the selector.

Figure 2: examples of SARDU-Net sub-protocol selection during training epochs in two distinct leave-one-out folds of the prostate data set. Measurements are reported along the horizontal axis; training epochs along the vertical axis; white/black flag measurements that were/were not selected. Sub-protocols that are 50% of the original length (i.e. 21 out of 42 measurements) were searched, with SARDU-Net free to select any DWI and a maximum echo time in LWI (up to and including all shorter TEs).

Figure 3: SARDU-Net reconstructions on prostate MRI. The top row shows examples of DWI/LWI images and apparent diffusion coefficient (ADC), kurtosis (K), luminal water fraction (LWF). The mid/bottom rows show images reconstructed by SARDU-net when 50% (mid row) or 33% (bottom row) of the input data were kept, and ADC, K, LWF obtained from signal reconstructions. A lesion is highlighted by a red arrow. SARDU-Net predictions are shown only within the prostate.

Figure 4: examples of SARDU-Net sub-protocol selection during training epochs in two distinct leave-one-out folds of the spinal cord data set. Measurements are reported along the horizontal axis; training epochs along the vertical axis; white/black flag measurements that were/were not selected. Sub-protocols that are 50% of the original length (i.e. 49 out of 98 measurements) were searched, with SARDU-Net free to select any image across various contrasts.

Figure 5: SARDU-Net reconstructions on spinal cord MRI. The top row shows examples of ZOOM-EPI images and fractional anisotropy (FA), T1, T2 and magnetisation transfer ration (MTR). The mid and bottom rows show examples of images reconstructed by SARDU-net when 50% (mid row) or 33% (bottom row) of the input data were kept, and FA, T1, T2, MTR obtained from the SARDU-Net signal reconstructions. SARDU-Net predictions are shown only within the cord.

Proc. Intl. Soc. Mag. Reson. Med. 28 (2020)

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