Release from fractal matrices

The Weibull Function Describes Drug Release from Fractal Matrices 

We thus expect a differential equation of the form of (4.13) to hold, where a is a proportionality constant, g (f) n (t) denotes the number of particles that are able to reach an exit in a time interval dt, and the negative sign denotes that n (f) decreases with time. This is a kinetic equation for an A + B - B reaction. The constant trap concentration [5] has been absorbed in the proportionality constant a. The basic assumption of fractal kinetics [16] is that g(t) has the form g (t) oc I,, L. In this case, the solution is supplied by (4.14). 

The form of this equation is a stretched exponential. In cases in which a system can be considered as infinite (for example, release from percolation 

The above reasoning shows that the stretched exponential function (4.14), or Weibull function as it is known, may be considered as an approximate solution of the release problem. The advantage of this choice is that it is general enough for the description of drug release from vessels of various shapes, in the presence or absence of different interactions, by adjusting the values of the parameters a and b. Monte Carlo simulation methods were used to calculate the values of the parameters a and (mainly) the exponent b [87]. 

These results reveal that the same law describes release from both fractal and Euclidean matrices. The release rate is given by the time derivative of (4.14). For early stages of the release, calculating the derivative of (4.14) and performing a Taylor series expansion of the exponential will result in a power law for the 

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Figure 4.12 shows simulation results (line) for the release of particles from a fractal matrix with initial concentration Co = 0.50, on a lattice of size 50 x 50. The simulation stops when more than 90% of the particles have been released from the matrix. This takes about 20, 000 MCS. In the same figure the data by... 

Computer simulations are useful tools in the study of drag release from matrix platforms, especially because they can describe the profile through the whole process. The used equation by Villalobos and al. is a useful model to describe the release profiles generated from both fractal and Euclidian stracmres, and can be properly applied to the one-dimensional case but future efforts are necessary to relate theoretical values with experimental results, such way determination to give a straightforward idea of the internal structure of the platform and vice versa (Villalobos et al. 2009). 

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