This experiment involves encapsulating silk protein material with the product we express, and observing its release rate under simulated physiological environmental conditions.
Due to limited time, knowledge, and resources, our model is relatively simple.
Through mathematical modeling using codes, we can simulate the environmental factors of microneedles to observe their quality. At the same time, this is also to verify future efficiency, so we need to use mathematical modeling to predict future quality.
Our idea is to use a simple ordinary differential equation to model the result data
where 𝑏 represents the degradation rate and should be negative, and 𝑐 is the threshold ratio at which the degradation will not occur anymore.
The equation has a unique solution
Now, we use least square regression for the model to determine the unknown parameters 𝑏, and 𝑐, and solve the optimization problem with 𝑛=16 experimental data (to simplify, we let 𝑑=𝑏𝑐 here)
We use MATLAB to plot the fitting curve. The codes we used are shown in the following graph:
Figure 1. Codes in MATLAB.
Running the codes above in MATLAB, we get the final curve below:
Figure 2. Exponential Fitting Curve for The Mass Remained.
In our experiments, the microneedle patch with the expressed system are placed in a simulated body fluid environment. Based on the exponential fitting result for the mass remained, the quality of the microneedles is monitored at different times because they gradually disintegrate, resulting in a decrease in the quality of the microneedles.
As seen in the results, our model shows that microneedle's quality is tracked over time as it deteriorates.
However, considering the differences between the experimental environment and the actual production environment, as well as our simplification of the model and data, the actual results may differ slightly from the model. Therefore, we still need to improve our model and find more accurate ways for our model. Further experimental investigations should also be done to reduce the margin of error between the real production results and the experimental modeled one.
What we can provide for the future teams is the overall modeling approach and the approximate fitting curve results.