Chapter 7 - Math Model

The rate of release is most likely dependent on three factors: time, the concentration of dye in the hydrogels, and the concentration of gel in solution. The results, as plotted below, suggest an exponential model which is dependent only on the concentration of dye in the hydrogel. Because the release approaches nearly 1, the concentration of dye in solution, if it has an effect, would manifest its effect toward the end of trial when the concentration gradient between the dye and the solution is greatest. These considerations suggest that the model described in the below MATLAB analysis is likely accurate. The coefficients in the exponential models, represented by the slopes of the regressions done in week 6, can be plotted against the concentrations of sodium alginate used to prepare the beads to form another regression that can be used to predict the release coefficient for other concentrations. This model could also then be used determine an appropriate concentration of alginate used to prepare beads for a desired release rate.

Flipping the axes allows prediction based on release rate. Because it is the same data, the Coefficients of Correlation and Determination will be the same.

More data points would increase not only the confidence bounds but also the domain for interpolation. Each trial takes over an hour of constant measurements however making it necessary to balance number of trials with domain and confidence.