Frequency of mean transit times vs. time

Overall, the biased random walk, which places more emphasis on the motion toward the output end and less on the other directions, mimics more closely the transit profile of the experimental data. Both diffusion models, i.e., the blind and the myopic ant models, can reproduce the basic features of the real small-intestinal transit profile. 

The probabilistic absorption model described herein [217] was based on the cylinder built in [216] that incorporates all the random heterogeneities that 

A tablet, which is modeled as an aggregate of drug particles of mass qo, is inserted in one end of the tube (input end). At each time step a portion of the mass of the tablet can be dissolved. The rate of dissolution is considered to be dependent on three factors, which are all expressed in probability values. 

The first factor, kd, mimics the conventional dissolution rate constant it is inherent for every drug and takes values in the range 0 kdi 1. A value close to unity denotes a drug with rapid dissolution characteristics. Thus, a specific kdi value is conceived for a given drug under certain experimental conditions. As a probability value, kd corresponds to pd and it expresses the number of events occurring in a time unit. Consequently, kd has dimension of time-1. 

The second factor, kc, is related to the first-order concentration dependence of the dissolution rate. As dissolution proceeds the amount of drug in solution increases exponentially and therefore the value of kc is reduced exponentially. This reduction is controlled by the relative amount dissolved, q (t) /qs, as defined in Section 5.1.4, at each time point  

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Figure 6.12 Frequency of mean transit times vs. time (min) using the diffusion model II for the blind ant model positions for various concentrations of villi and forward probabilities pf values. Key experimental data solid line, TVvini = 200 and pf = 0.6 dashed line, Nvnn = 200 and pf = 0.5 dotted line, Nvmi = 180 and pf = 0.7 dashed-dotted line, TVviin = 180 and pf = 0.5.

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