The aim of this study is to extend the AMICO¹ (Accelerated Microstructure Imaging via Convex Optimisation) framework to the VERDICT^2,3 (Vascular, Extracellular, and Restricted Diffusion for Cytometry in Tumours) model-based diffusion-weighted MRI (DW-MRI) technique and to evaluate its performance in the clinical application for prostate cancer imaging.

Prostate cancer is the most common cancer among men in all economically developed countries⁴. A non-invasive method of diagnosis and grading would revolutionise clinical practice. VERDICT, a model-based technique, for characterising microstructural tissue parameters has shown promise in preclinical studies² and in a pilot clinical setting³ for discriminating normal and malignant prostate tissue. However, VERDICT uses a computationally expensive non-linear fitting procedure to estimate model parameters from the data, which limits its use in large cohort studies and real-time clinical applications. Recently, ultrafast fitting algorithms, such as the AMICO framework, have been developed to address the computational cost of model-based microstructure-imaging techniques. Through linearization and convex optimisation, AMICO reduces dramatically the computational cost of microstructure imaging techniques in the brain and locates the global minimum parameter values more reliably.

4 subjects suspected for prostate cancer with a previous multiparametric prostate MRI (mpMRI) were scanned for VERDICT analysis. For each subject DW-MRI was performed using a 3T scanner (Achieva, Philips Healthcare, Netherlands) using a pulse-gradient spin-echo sequence and a 32 channel cardiac coil with b values of 90-3000s/mm in 3 orthogonal directions,⁵ the imaging parameters are summarised in Table 1. Data was normalised with a b=0 image for every echo time to avoid T2 dependence. In one case (subject 4), the scan was repeated after a 2-minute interval.

MR datasets were analysed with Osirix Version 7.0 (Bernex, Switzerland). For each subject a board certified radiologist (EJ) manually contoured three regions of interest (ROIs): (1) the whole prostate, (2) a region corresponding to tumour tissue and (3) a region for normal tissue on the same slice.

The VERDICT model was fitted to the data in each voxel using both the original non-linear fitting algorithm (_ORIGINALVERDICT) and the AMICO framework adapted for VERDICT (_AMICOVERDICT). _ORIGINALVERDICT uses an iterative optimization procedure^2,3 that accounts for local minima and Rician noise, as implemented in the open-source Camino toolkit.⁶ _AMICOVERDICT expresses the VERDICT model as a linear system and leading to a convex optimization problem, which is solved to fit the model to the data using freely available code (https://github.com/daducci/AMICO/).¹ Both procedures fit the same set of parameters.

The time required to fit the models to the data is compared. For subject 4 the repeatability of both models was also tested. All the experiments have been conducted on a 3.1 GHz Intel Core i7, 8 GB ram DDR3, without multi-threading or parallel computing.

Subjects’ ages range 62.7 to 74.4 years. In all cases a biopsy performed within a week of the scan confirmed cancer with Gleason scores⁷ of 3+4. The computation time for VERDICT is reduced with the _AMICOVERDICT formulation, from 1.18s/voxel to 0.78ms/voxel, the exact time required to compute the parameter maps is reported in Table 2.

Figure 1 shows that _AMICOVERDICT parameter maps are more homogeneous (less noisy) than those obtained with the original fitting. This is most likely because AMICO is less sensitive to local minima – the more homogeneous minimum objective function maps (the numerical values are not directly comparable) support this. Both models show similar differences in parameter values between tumour and normal tissue, for example, in both cases fIC (Intracellular volume fraction) is higher and fEES (Extracellular-Extravascular volume fraction) is lower in tumour tissue compared with normal tissue. However, the numerical values in Figure 2 show differences between the two estimation procedures, although both estimates are physiologically plausible. Both procedures provide similar reproducibility between acquisitions as illustrated in Figure 3.

The principal benefit of the AMICO framework is that provides an acceleration factor of several orders of magnitude compared with non-linear fitting, which we demonstrate here for the VERDICT model. AMICO may also achieve more robust and repeatable parameter estimates, although further work on a larger cohort and comparison against histology is required to test this. Improved location of the global minimum parameter values may also enable relaxation of some of the assumptions in the VERDICT model, such as fixed diffusivities and zero permeability, thus supporting more detailed and accurate microstructural assessment – future work will also evaluate this possibility.

To conclude, _AMICOVERDICT reflect the microstructural differences between tumours and normal tissue in a clinically practical time. Results should be evaluated in larger cohorts to test the parameters correlation with cancer grade.