  Purpose: Demonstrating and assessing self-supervised machine learning fitting
of the VERDICT (Vascular, Extracellular and Restricted DIffusion for Cytometry
in Tumours) model for prostate. Methods: We derive a self-supervised neural
network for fitting VERDICT (ssVERDICT) that estimates parameter maps without
training data. We compare the performance of ssVERDICT to two established
baseline methods for fitting diffusion MRI models: conventional nonlinear least
squares (NLLS) and supervised deep learning. We do this quantitatively on
simulated data, by comparing the Pearson's correlation coefficient,
mean-squared error (MSE), bias, and variance with respect to the simulated
ground truth. We also calculate in vivo parameter maps on a cohort of 20
prostate cancer patients and compare the methods' performance in discriminating
benign from cancerous tissue via Wilcoxon's signed-rank test. Results: In
simulations, ssVERDICT outperforms the baseline methods (NLLS and supervised
DL) in estimating all the parameters from the VERDICT prostate model in terms
of Pearson's correlation coefficient, bias, and MSE. In vivo, ssVERDICT shows
stronger lesion conspicuity across all parameter maps, and improves
discrimination between benign and cancerous tissue over the baseline methods.
Conclusion: ssVERDICT significantly outperforms state-of-the-art methods for
VERDICT model fitting, and shows for the first time, fitting of a complex
three-compartment biophysical model with machine learning without the
requirement of explicit training labels.
