Modeling

Because the biodegradable hydrogel used to carry our EcnB peptide has several tunable properties including rate of biodegradation and internal concentration of EcnB, we decided to model the distribution of the peptide throughout the fish in order to better understand what properties we want in the gel. This model was divided into the drug’s two main components, the EcnB and the hydrogel. Both parts were designed using COMSOL Multiphysics.

Part 1: Necessary concentrations of EcnB in the fish

Knowing the EcnB concentration necessary to combat Flavobacterium alone, we worked backwards to determine an effective EcnB concentration in the salmon bloodstream. We modelled the convection, diffusion, and degradation of the peptide through blood vessels, muscle tissue, and the skin of an idealized 2D fish. We estimated necessary parameters, including the metabolic elimination rate of fish based on field data from average-sized Atlantic salmon [1].

We found a target EcnB concentration in the blood for a predefined concentration range on the skin by adjusting initial concentration parameters of the bloodstream. The target concentration of EcnB on the skin was bounded by the minimum effective concentration against Flavobacterium and the toxic concentration of EcnB in the fish. Our goal was an upwards of 5x10¹⁴ mol/m³ of EcnB at skin level [2]. However, due to the combination of small length and large time scales, our model had difficulty generating a solution. We decided to continue with the second part of the model, but using representative parameter values rather than experimental.

Part 2: Properties of the hydrogel

The purpose of this second model was to find our ideal hydrogel degradation rate and peptide concentration for proper treatment of BCWD. We simulated hydrogel diffusion through the fish to determine the resultant concentration of EcnB peptide within a fish, assuming that all of the EcnB peptide within the gel is transferred into the subcutaneous layer of the fish. We decided on a 3D model for this part because the fish tag has some odd geometries and isn’t actually symmetric. We used SolidWorks to build the hollow of the fish tag into which we would fill the gel. The opening of the tag was modelled as an open boundary, meaning the fish is large enough that concentrations of the peptide within the fish is negligible. Because our 2D model hadn’t provided reasonable answers to formulate a target outward flux from the tag, we decided to make a representative model instead. We were more interested in seeing the changes in concentration gradient than the actual values of concentration.

Figure 1: The initial setup of the Part 2 model, showing the concentration of EcnB within the fish tag. The peptide exists only within the gel to start with.

Figure 2: The Part 2 model after some time has passed. The gel has only degraded a short way through, but there is enough peptide to maintain a high flux into the fish.

Figure 3: The Part 2 model after a longer time has passed. The degraded gel face has moved farther back, but the peptide concentration remains high throughout the entire tag.

As can be seen in figures 2 and 3, the fish tag can maintain a high outflow concentration that approaches the initial gel concentration. This is a consequence of the drastic narrowing of the tag near the tip. One unexpected result is the gradual increase in outflow concentration as the gel degrades. More and more peptide is released but, due to the small opening, there is a limit on how fast the peptide can diffuse out of the tag.

References

[1] Clark, K., Gobas, F., & Mackay, D. (1990). Model of Organic Chemical Uptake and Clearance by Fish from Food and Water. Environmental Science & Technology, 24.

[2] Schubiger, C., Orfe, L., Sudheesh, P. Cain, K., Shah, D., & Call, D. (2015). Entericidin is required for a probiotic treatment to protect trout from cold-water disease challenge. Applied and Environmental Microbiology, 81(2), 658-65.