Quantification of Articular Cartilage Microstructure by the Analysis of the Diffusion Tensor

Abstract

In this chapter, we present approaches to the 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 magnetic resonance imaging (MRI) data into quantitative microstructural and compositional characteristics of articular cartilage. The chapter begins with a brief introduction to diffusion nuclear magnetic resonance and diffusion imaging, focusing 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.

Physical Properties of Cartilage by Relaxation Anisotropy

“…Purely theoretical work on relaxation anisotropy of articular cartilage still remains scarce. Only a few articles pertaining to Redfield relaxation theory, either analytically using different motional models 53 , or by a full numerical calculation of spectral densities 54 , or utilizing Monte Carlo simulations 55 in cartilage can be found. Considering the current hardware and software resources targeted for purely computational and theoretical NMR/MRI work, this field is expected to grow in the future.…”

Translational and Rotational Dynamics of Water Molecules in Aligned Collagenous Tissues: Implications for Assessing Collagen Organisation with Magnetic Resonance Imaging

“…The paper presents the application of the model to experimental articular cartilage data to interpret diffusion anisotropy in terms of the model fibre orientation distribution. This work and other related studies from our research group, was the basis for a book chapter [57] currently in press, presented in Appendix 2.…”

“…The definition of the network can vary from rigid cylinders [62,63,191,195,196], analogous to model fibres, to networks of crosslinked cylinder segments [188][189][190]. A more detailed overview on constructing the fibre networks can be found in Appendix 2 [57], along with a discussion on the Langevindynamics method for incorporating water-fibre interactions [63]. In any case, the key parameters of the fibre network are the fibre volume fraction, which can be controlled via the number or radii of the cylinder segments, and the overall alignment of the network.…”

“…In the case of aligned networks, the restriction to diffusion caused by bonding can be easily subtracted from the total restriction, to reveal the restriction cause by obstruction alone [62]; but this is not easily achieved in non-aligned networks. Simulations of water through networks, like those presented in Chapter 4, can also be thought of as implicitly modelling water-proteoglycan (PG) interactions [57,63]. Although PGs do not contribute to diffusion anisotropy (they show no global alignment in the extracellular matrix (ECM) [38,47,54,220]), they do contribute to restricting the diffusion of water molecules through both obstruction and hydrogen bonding.…”