Modeling Drug Transit in the Intestines

The small-intestinal transit flow is a fundamental process for all gastrointestinal absorption phenomena. However, the structure of the gastrointestinal tract is highly complex and it is practically impossible to explicitly write and solve the equations of motion for the drug flow. Instead, numerical computer simulation techniques that incorporate the heterogeneous features of the gastrointestinal wall structure and of the drug flow are used in this section to characterize the intestinal transit process in humans. 

An algorithm is built from first principles, where the system structure is recreated and subsequently the drug flow is simulated via Monte Carlo techniques [216]. This technique, based on principles of statistical physics, generates a microscopic picture of the intestinal tube. The desired features of the complexity are built in, in a random fashion. During the calculation all such features are kept frozen in the computer memory (in the form of arrays), and are utilized accordingly. The principal characteristic of the method is that if a very large number of such units is built, then the average behavior of all these will approach the true system behavior. 

The model is based on a cylinder whose length is several orders of magnitude larger than its radius. Thus, any entanglements that are present are ignored, 

Two different models of the biased random walk were envisaged. In model 

2 direction, the probability toward the output end (z+) is now (I/2) + e, while the corresponding probability toward the input end (z ) is (1/z) — e (where 2 is the coordination number of the underlying space, e.g., z = 6 in a 3-dimensional space). This model has the characteristic that diffusion is equally probable in all possible directions, the species spending equal times in all of them, but due to the factor, when the 2 direction is chosen a positive flow drives the solution to the output end. 

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