Background

Viscosupplementation is one of the most common forms of arthritis therapy. It involves injecting a lubricant into the joint to restore the viscosity of the synovial fluid. However, viscosity was found to be a poor predictor of the clinical performance of these materials. Instead, lower friction coefficient correlated well with assessments of improved clinical function. Therefore, the aim of arthritis therapy should be to reduce friction rather than focusing on viscosity. 

Viscosity and coefficient of friction are related via the Stribeck framework. Friction coefficient is a function of the Sommerfeld number, which is a dimensionless parameter equal to the product of sliding speed, viscosity, and contact width divided by normal force (S = v * η * d / N). However, there are exceptions to this framework. Some non-viscous materials lubricate as if they are viscous. They have a much lower coefficient of friction than their measured viscosity predicts, which means they deviate from the Stribeck curve. In order to reconcile this, the Sommerfeld number is increased by orders of magnitude to match the friction coefficient. This adjustment involves replacing measured viscosity by a mathematical tool called effective viscosity (ηEff) when calculating the Sommerfeld number.

Effective viscosity could be more than just a mathematical tool, however. It could be a legitimate physical phenomenon where there is a localized increase in viscosity right next to the articular surface due to entanglements with native lubricin. This change in localized viscosity could be examined by suspending fluorescent beads in lubricant in the presence of cartilage and observing their Brownian motion (i.e., the random movement of particles suspended in fluid). Viscosity is inversely proportional to the speed of the beads due to increased resistance to movement.

Aim

Determine how the viscosity of mimetic lubricin (Pleryon) changes with respect to distance from the articular surface. 

Hypothesis

The viscosity of mimetic lubricin will be greater near the articular surface than everywhere else. 

Methods

• Suspend beads in lubricant. Add a piece of cartilage.

• Record Brownian motion of beads on Zeiss i880 microscope. Videos were taken 0 μm, 50 μm, 100 μm, 200 μm, and 500 μm away from the articular surface. 

• Input videos into Trackpy (Python package that analyzes the trajectory of the beads), which outputs parameter A.

• Plug A into diffusivity constant equation to find diffusivity constant (D). D = A / 4 

• Plug D into Stokes-Einstein equation to find viscosity (η). η = (KB * T) / (6 * π * D * r)

Fixing Trackpy

Trackpy was generating highly errant trajectories and viscosity values at the beginning of the semester. Additionally, it was not clear what was causing the errors. Therefore, it was necessary to examine the Trackpy algorithm step-by-step and modify the code to rectify the errors.

In order to troubleshoot, I coded an animation of how Trackpy generated trajectories in real time. This animation could then be compared side-by-side with the input video to determine whether the Trackpy trajectories matched the viewer’s intuition. The animation revealed that Trackpy often tracked “particles” that could not be seen by the viewers. This was fixed by optimizing the size, mass, and eccentricity filters. 

Trackpy was now reliable in terms of tracking the overall (random + non-random) motion of the particles. However, it still generated drastic “jumps” when plotting the Brownian (random) component of motion, and the A values were still wildly incorrect. Therefore, the error occurred when drift (non-random) was subtracted from overall motion to isolate Brownian motion. It turned out that Trackpy incorrectly set drift = 0 for certain frames of the video when there was a low concentration of particles. Hence, I modified the drift subtraction function to remove the errant zeros. The Trackpy results were now trustworthy and accurate. 

Experiment 1 - What is the viscosity of PBS and BSF? 

This experiment was performed to ensure that Trackpy was outputting the correct values for lubricants in the absence of cartilage (n = 3). The viscosity of PBS was 1.00632 ± 0.0198 mPa*s, and the viscosity of BSF was 97.61 ± 5.425 mPa*s. These outputs matched the expected values for both fluids. 

Experiment 2 - Does bead size affect viscosity? 

This experiment was performed to ensure that Trackpy output was correct regardless of the size of beads. Therefore, 200 nm and 500 nm diameter beads were suspended in BSF (n = 3). The mean for the 200 nm group was 97.61 mPa*s. The mean for the 500 nm group was 90.88 mPa*s. The error bars overlapped, meaning viscosity of BSF was not significantly affected by bead size. 

Experiment 3 - Does bead concentration affect viscosity?

This experiment was performed to ensure that Trackpy output was correct regardless of the concentration of beads. Therefore, 500 nm beads were diluted by factors of 1:80, 1:100, and 1:120 in PBS (n = 3). The mean for the 1:80 dilution group was 1.0202 mPa*s. The mean for the 1:100 dilution group was 0.9810 mPa*s. The mean for the 1:120 dilution group was 1.0094 mPa*s. The error bars overlapped, meaning viscosity of PBS was not significantly affected by bead concentration. 

Experiment 4 - Does viscosity of PBS increase near cartilage? 

This experiment was performed to detect any changes in PBS viscosity with respect to distance from the articular surface. Therefore, 500 nm beads were suspended in PBS with cartilage. Videos were recorded 0 μm, 50 μm, 100 μm, 200 μm, and 500 μm away from the articular surface (n = 2).

When cartilage was placed in PBS, there was a layer of beads completely adherent to the articular surface. This would seem to be evidence of a dramatic increase in viscosity near the cartilage. However, this was unexpected because PBS does not display effective viscosity on a tribometer. The mechanism behind the attachment was unknown, so it was decided to exclude the adherent beads from the dataset. Thus, viscosity was analyzed 10 μm away from the cartilage instead of 0 μm. The localized viscosity of PBS remained constant regardless of distance from the cartilage. However, the first 10 μm away from the articular surface need to be re-examined in a future experiment. 

Experiment 5 - Does viscosity of mimetic lubricin (Pleryon) increase near cartilage? 

This experiment was performed to detect any changes in mimetic lubricin’s viscosity with respect to distance from the articular surface. Therefore, 500 nm beads were suspended in mimetic lubricin with cartilage. Videos were recorded 0 μm, 50 μm, 100 μm, 200 μm, and 500 μm away from the articular surface (n = 2).

Similar to PBS, there was a layer of beads completely adherent to the articular surface. The adherent beads were excluded from the dataset. Thus, viscosity was analyzed 10 μm away from the cartilage instead of 0 μm. The localized viscosity of mimetic lubricin remained constant regardless of distance from the cartilage. However, the first 10 μm away from the articular surface need to be re-examined in a future experiment. 

Conclusions

• Trackpy outputs the viscosity of PBS as 1 mPa*s and BSF as 100 mPa*s, which matches the expected values. 

• Trackpy’s output viscosity values are unaffected by bead size.

• Trackpy’s output viscosity values are unaffected by bead concentration. 

• The viscosity of both PBS and mimetic lubricin remains constant from 10 μm to 500 μm away from cartilage. However, the 0-10 μm range needs to be examined further once the mechanism behind bead adherence is properly understood. 

Future Directions

The main limitation of this study was that the beads were completely attached to the surface of cartilage when it is immersed in both PBS and mimetic lubricin. The PBS case was particularly surprising because PBS did not display effective viscosity when examining tribological measurements. Since the mechanism of attachment was unknown, data from the first 10 μm away from the cartilage surface were excluded. 

In order to isolate the factor that is causing the attachment, it is necessary to repeat the experiments with specific modifications. The first repetition of the experiment should consist of using unmodified beads instead of carboxylate-modified beads to eliminate the errant chemical interactions from the carboxylate. The second repetition of the experiment should consist of using lubricin-removed cartilage to determine whether the adherence persists in the absence of lubricin.

Additionally, a wider range of lubricants should be used in the future. Examples include hyaluronic acid, low-viscosity microgels, and recombinant lubricin. Testing a greater diversity of materials will provide better insights into how lubricants’ properties (size, hydrophobicity, functional groups, etc.) influence interactions with the articular surface of cartilage.

Figure References

a. Trujillo, R. J., Tam, A. T., Bonassar, L. J., & Putnam, D. (2023). Effective viscous lubrication of cartilage with low viscosity microgels. Materialia, 33, 102000. https://www.sciencedirect.com/science/article/pii/S2589152923003277?via%3Dihub. 

b. Bonnevie, E. D., Galesso, D., Secchieri, C., Cohen, I., & Bonassar, L. J. (2015). Elastoviscous Transitions of Articular Cartilage Reveal a Mechanism of Synergy between Lubricin and Hyaluronic Acid. PLOS ONE, 10(11), e0143415–e0143415. https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0143415.