Fractional Diffusion in Drug Transport: A Caputo Framework for Non-Fickian Dynamics and Heterogeneous Absorption

Resumen

We already know that predicting how drugs move in living tissue is hard. In complex biological systems, the weird spread of anomalous diffusion really happens and is delayed; standard models are not good at capturing that, it’s like the tissue has memory.
Accordingly, we adopted a fractional calculus model that was more sophisticated in this work. This model, which employs a tool known as a Caputo derivative, allows for that memory effect and the sluggish, non-standard way drugs often spread, something called sub-diffusion. We did this in a realistic way where we let the rate of drug spread diffusion as well as the rate of the tissue soaking up or breaking down the drug absorption and spreading change over time and over location within the tissue, because real tissue is not uniform.
We modeled a common situation: a fast shot of a drug at one location. To crunch the numbers, we deployed some nifty computational techniques: one kind of algorithm captured the crucial memory element of the fractional math, and another dealt with spatial spread calculations. We performed these simulations at a variety of grid sizes to test the accuracy of our results.
What did we uncover? This fractional model does indeed describe the delay and the drug concentration left in real biological tissues. Its location matters significantly, because we saw that when, where and how much tissue absorbs the drug has a say in where the drug goes. It's a reminder that fractional math is not just an abstraction; it's central to understanding actual drug behavior in the body. It provides a much better tool for designing smarter drug delivery devices that can operate along with the body’s complex biochemistry. This work sets a strong computational base that can be used in future to model even more complex biological drug delivery contexts