Direct Osmotic Pressure Measurements in Articular Cartilage Demonstrate Nonideal and Concentration-Dependent Phenomena

The osmotic pressure in articular cartilage serves an important mechanical function in healthy tissue. Its magnitude is thought to play a role in advancing osteoarthritis. The aims of this study were to: (1) isolate and quantify the magnitude of cartilage swelling pressure in situ; and (2) identify the effect of salt concentration on material parameters. Confined compression stress-relaxation testing was performed on 18 immature bovine and six mature human cartilage samples in solutions of varying osmolarities. Direct measurements of osmotic pressure revealed nonideal and concentration-dependent osmotic behavior, with magnitudes approximately 1/3 those predicted by ideal Donnan law. A modified Donnan constitutive behavior was able to capture the aggregate behavior of all samples with a single adjustable parameter. Results of curve-fitting transient stress-relaxation data with triphasic theory in febio demonstrated concentration-dependent material properties. The aggregate modulus HA increased threefold as the external concentration decreased from hypertonic 2 M to hypotonic 0.001 M NaCl (bovine: HA=0.420±0.109 MPa to 1.266±0.438 MPa; human: HA=0.499±0.208 MPa to 1.597±0.455 MPa), within a triphasic theory inclusive of osmotic effects. This study provides a novel and simple analytical model for cartilage osmotic pressure which may be used in computational simulations, validated with direct in situ measurements. A key finding is the simultaneous existence of Donnan osmotic and Poisson–Boltzmann electrostatic interactions within cartilage.

Implementation of Finite Deformation Triphasic Modeling in the Finite Element Code FEBio

Many biological soft tissues exhibit a charged solid matrix, most often due to the presence of proteoglycans enmeshed within the matrix. The predominant solute content of the interstitial fluid of these tissues consists of the monovalent counter-ions Na+ and Cl−. The electrical interactions between the mobile ion species and fixed charge density of the solid matrix produces an array of mechano-electrochemical effects, including Donnan osmotic swelling, and streaming and diffusion potentials and currents. These phenomena have been successfully modeled by the triphasic theory of Lai et al. [1], which is based on the framework of mixture theory [2]. Other similar frameworks have also been proposed [3, 4]. The equations of triphasic theory are nonlinear, even in the range of infinitesimal strains. Therefore, numerical schemes are generally needed to solve all but the simplest problems using this framework.

Three-Dimensional Finite Volume Method of Triphasic Theory in Generalized Coordinates: Application to Human Intervertebral Disc During Compressive Stress Relaxation

The intervertebral disc is an avascular cartilaginous structure that plays an important role in supporting loads through the spine and providing flexibility to the spinal column. The triphasic theory [1,2] has been used successfully to describe many of the mechanical, chemical and electrical behaviors of cartilaginous tissues. As an example of applying the triphasic theory, Yao and Gu [3] conducted a finite element simulation of human intervertebral disc during compressive stress relaxation using commercial software (FEMLAB). Due to the limitation of the commercial software, in the simulation reported in [3], the computational grid (mesh) is fixed throughout the simulation and the mesh size was not optimized for the specific geometry of the disc.

On the Thermodynamical Admissibility of the Triphasic Theory of Charged Hydrated Tissues

The triphasic theory on soft charged hydrated tissues (Lai, W. M., Hou, J. S., and Mow, V. C., 1991, “A Triphasic Theory for the Swelling and Deformation Behaviors of Articular Cartilage,” ASME J. Biomech. Eng., 113, pp. 245–258) attributes the swelling propensity of articular cartilage to three different mechanisms: Donnan osmosis, excluded volume effect, and chemical expansion stress. The aim of this study is to evaluate the thermodynamic plausibility of the triphasic theory. The free energy of a sample of articular cartilage subjected to a closed cycle of mechanical and chemical loading is calculated using the triphasic theory. It is shown that the chemical expansion stress term induces an unphysiological generation of free energy during each closed cycle of loading and unloading. As the cycle of loading and unloading can be repeated an indefinite number of times, any amount of free energy can be drawn from a sample of articular cartilage, if the triphasic theory were true. The formulation for the chemical expansion stress as used in the triphasic theory conflicts with the second law of thermodynamics.

Effects of Compression on Distributions of Oxygen and Lactate in Intervertebral Disc

Since the intervertebral disc (IVD) is the largest avascular cartilaginous structure in the human body, poor nutrient supply has been suggested as a potential mechanism for disc degeneration. The previous theoretical studies have shown that the distributions of nutrients and metabolites (e.g., oxygen, glucose, and lactate) within the IVD depended on tissue diffusivities, nutrient supply, cellular metabolic rates, and coupling effects between nutrient and metabolite [1,2]. Our recent theoretical study suggested that dynamic compression can promote transport of neutral solute in the anisotropic cartilaginous tissue by enhancing both diffusive and convective solute fluxes [3]. However, the effect of compression on distributions of nutrients and metabolites in the IVD has not been studied. The objective of this study was to examine the effects of compression on distributions of oxygen and lactate in the IVD under static and dynamic unconfined compression using a new formulation of the triphasic theory.