An Experimental and Finite Element Protocol to Investigate the Transport of Neutral and Charged Solutes across Articular Cartilage

The overall goal of this procedure it to investigate the transport of charged and uncharged molecules across articular cartilage with the aid of experimental and numerical methods. This method can help answer key questions related to physical properties of articular cartilage, such as diffusion coefficient and fixed charge density in different zones. The main advantage of this technique is that it adopts a finite path, experimental model based on microcomputer tomography of transport of radiopaque molecules.

To begin sample preparation, drill out an 8.5 millimeter diameter cylindrical osteochondral plug while spraying room temperature phosphate buffered saline, PBS, onto the drilling area. Insert the plug into an approximately 2.5 centimeter length of heat shrink tubing so that the bone layer is flush with the end, and then cover the cartilage surface with wet cotton. Then use a hot air gun to shrink the tubing around the sides of the plug.

Load a finite volume of a 420 millimolar ioxaglate or iodixanol solution onto the cartilage surface inside the tubing to prepare a negatively charged or neutral solute bath respectively. Seal the open end of the tube with a cork. Place the sample with the corked end up on a sample holder mounted on the motorized stage of a micro-CT.

Scan over a field of view containing the cartilage, subchondral plate, and finite bath. Repeat the scan periodically over the next 48 hours or until the contrast agent concentration in the cartilage does not change over time. In the instrument software, register the 3-D images at different time points relative to the initial image and convert the reconstructed images to a 2-D TIFF file stack.

Import the images into an image processing program and duplicate them to segment bath and subchondral bone separately. Next, holes in the subchondral bone are filled and redundant pixels in the bath are removed manually. The resulting segmented bath and subchondral bone images are then added mathematically.

And using the wand tool, the outline of the cartilage mask is defined and added to the Region of Interest Manager. Measure the average gray value of the cartilage. Based on the initial concentrations in the bath and cartilage, convert the average gray values in the bath and cartilage to solute concentration using a linear calibration curve.

Plot the solute concentrations over time. To begin the computational modeling of diffusion using FEBio software, build finite bath-based cartilage multi-zone models where the superficial zone comprises 20%of the cartilage thickness, the middle zone represents 50%and the deep zone represents 30%A table containing the information of a neutral solute is created for a Biphasic Solute model. And a table containing the information of charged solutes is created for a Multiphasic model.

To model the diffusion of charged solutes with the Multiphasic model, two monovalent counter-ions to both the bath and the cartilage have to be added to avoid the effects of electric fluctuation between the bath and the tissue. Once the cartilage and finite bath zones have been modeled, assign the corresponding mechanical and physical properties, namely, Young's modulus, permeability, free diffusivity, and diffusivity to each zone for the Biphasic Solute model. Assign mechanical and physical properties, namely, Young's modulus, permeability, free diffusivity, and diffusivity, as well as fixed charge density to each zone for the Multiphasic model.

Next, generate an eight node trilinear hexahedral element mesh and refine it near the boundaries. To model the diffusion of neutral solutes with the Biphasic Solute model, apply the initial solute concentration and effective pressure to the Finite Bath model. Run the Biphasic Solute model in transient mode to produce solute concentration versus time curves based on the diffusion coefficients for each cartilage zone.

For the Multiphasic model in a steady state step, set the same effective fluid pressures and solute concentrations for the cartilage and finite bath while increasing fixed charged density to its desired value. In a transient step, create a well stirred finite bath by keeping the diffusion coefficient in the bath sufficiently high. Inject the solute from the bath air interface into the bath to reach the concentration value.

Then remove the prescribed solute concentration boundary condition from the previous step and revert the diffusion coefficient of the finite bath to its actual diffusion coefficient. Run the Multiphasic model using an FEBio MATLAB interface to obtain solute concentration versus time curves based on applied fixed charge densities and the diffusion coefficients for each cartilage zone. Using this method, the diffusion processes of neutral an anionic contrast agents through articular cartilage were modeled with biphasic solute and Multiphasic models respectively.

Both models fit well with the experimental data. The diffusion coefficients of the neutral contrast agent, iodixanol, in different cartilage zones were determined from the Biphasic Solute model, and the diffusion coefficients of the anionic contrast agent, ioxaglate, in different zones were determined from the Multiphasic model. After its development, this technique paved the way for the researchers in the field of tissue biomechanics to explore the diffusive properties of soft tissues using a combination of experimental and computational approaches.

After watching this video, you should have a good understanding of how to design experimental and computational platforms regarding diffusion across articular cartilage.