Quantification of articular cartilage microstructure by the analysis of the diffusion tensor

In this Chapter, we present approaches to numerical simulation of the diffusion of water molecules in fibre networks that serve as models of articular cartilage. The simulations are intended as a tool for the translation of experimental diffusion MRI data into quantitative microstructural and compositional characteristics of articular cartilage. The chapter begins with a brief introduction to diffusion NMR and diffusion imaging, focussing on diffusion tensor imaging. It discusses the current limitations of diffusion MRI in quantifying articular cartilage microstructure beyond the predominant direction of collagen fibre alignment. We then detail the construction of aligned and partially aligned networks of fibres that can serve as models of articular cartilage. We discuss the methods for the simulation of the diffusion of tracer molecules through the model networks (especially Langevin Dynamics and Monte Carlo techniques), and reconstruction of the diffusion tensor from the simulated molecular trajectories. The aim of these simulations is to quantitatively link the eigenvalues and the fractional anisotropy of cartilage diffusion tensor to collagen fibre volume fraction and the degree of collagen fibre alignment. The global aim of this work is to move diffusion tensor imaging of articular cartilage beyond determination of the predominant direction of fibre alignment, and towards quantification of the fibre orientation distribution.