Transport of Neutral Solute Across Articular Cartilage: The Role of Zonal Diffusivities

Abstract

Transport of solutes through diffusion is an important metabolic mechanism for the avascular cartilage tissue. Three types of interconnected physical phenomena, namely mechanical, electrical, and chemical, are all involved in the physics of transport in cartilage. In this study, we use a carefully designed experimental-computational setup to separate the effects of mechanical and chemical factors from those of electrical charges. Axial diffusion of a neutral solute Iodixanol into cartilage was monitored using calibrated microcomputed tomography micro-CT images for up to 48 hr. A biphasic-solute computational model was fitted to the experimental data to determine the diffusion coefficients of cartilage. Cartilage was modeled either using one single diffusion coefficient (single-zone model) or using three diffusion coefficients corresponding to superficial, middle, and deep cartilage zones (multizone model). It was observed that the single-zone model cannot capture the entire concentration-time curve and under-predicts the near-equilibrium concentration values, whereas the multizone model could very well match the experimental data. The diffusion coefficient of the superficial zone was found to be at least one order of magnitude larger than that of the middle zone. Since neutral solutes were used, glycosaminoglycan (GAG) content cannot be the primary reason behind such large differences between the diffusion coefficients of the different cartilage zones. It is therefore concluded that other features of the different cartilage zones such as water content and the organization (orientation) of collagen fibers may be enough to cause large differences in diffusion coefficients through the cartilage thickness.

Combined inverse-forward artificial neural networks for fast and accurate estimation of the diffusion coefficients of cartilage based on multi-physics models

“…The descriptive details of the experiments consisting of sample preparation, image acquisition, and image processing are presented elsewhere (Arbabi et al, 2015b;Pouran et al, 2015). Osteochondral plugs (n=3, cartilage thickness= 2.8 mm, and diameter= 8.5 mm)…”

“…Occasionally mathematical fits have been used when analytical solutions were not available, however, since mathematical formulae involving diffusion coefficients are fitted to the experimental data, the physical importance of certain phenomena might be neglected (Kokkonen et al, 2011a). Computational models have been used to obtain the diffusion coefficient of neutral and charged solutes in complex geometries (Arbabi et al, 2015b;Ateshian et al, 2011). Nevertheless, computational models are often associated with optimization algorithms which require advanced computational expertise while being cumbersome and lacking the capacity to recognize pattern of the experimental data.…”

“…Previously, we described a finite-bath finite element model and derived the diffusion coefficients of a neutral solute across cartilage zones using direct scanning of the parameter space as the optimization algorithm (Arbabi et al, 2015b). We aim to create a package that can obtain the diffusion coefficients of a neutral solute in cartilage zones using series of micro-computed tomography (micro-CT) data even in labs where no computational expertise is available.…”

“…Molecular transport (diffusion) plays a key role in monitoring OA progression, delivery of therapeutics and nutrients as well as in the exchange of signaling molecules between cartilage and its surrounding tissues of subchondral bone and synovial fluid (Jackson and Gu, 2009;Pan et al, 2012;Pan et al, 2009). Previous studies used analytical solutions, mathematical fits, and computational models to derive the diffusion coefficients of solutes in cartilage (Arbabi et al, 2015b;Ateshian et al, 2011;Ateshian et al, 2012;Huttunen et al, 2014;Kokkonen et al, 2011a;Kokkonen et al, 2011b). The available analytical solutions can only be applied to problems where either simple geometries are used or simplified assumptions are made (Crank, 1979).…”

“…The rate of transport can be affected by the progression of the most common disease of diarthrodial joints, i.e. osteoarthritis (OA), which is due to changes in molecular structure of cartilage (Arbabi et al, 2015b;Huttunen et al, 2014;Ko and Quinn, 2013;Kokkonen et al, 2011a;Pouran et al, 2015). Molecular transport (diffusion) plays a key role in monitoring OA progression, delivery of therapeutics and nutrients as well as in the exchange of signaling molecules between cartilage and its surrounding tissues of subchondral bone and synovial fluid (Jackson and Gu, 2009;Pan et al, 2012;Pan et al, 2009).…”