Liver cancer is a leading cause of cancer-related death, and new quantitative MRI (qMRI) techniques are needed to inform treatment selection and monitor disease progression. We propose a new technique, Diffusion-Relaxation Hepatic Imaging via Generalisable Assessment of DiffusiOn Simulations (DR-HIGADOS), with the aim of improving sensitivity and biological specificity of liver qMRI. DR-HIGADOS is a diffusion-relaxation method that uses information from Monte Carlo simulations to map parameters of an extended intra-voxel incoherent motion model to microstructural indices (e.g. cell size, cellularity). DR-HIGADOS is demonstrated on multi-vendor clinical data, and its histological correlates are investigated on preclinical high-field scans.