Modeling drug release from an eroding matrix Hixson and Crow

Modeling drug release from an eroding matrix: Hixson and Crowell developed a model for drug release from a matrix that degrades via surface erosion. The Hixson-Crowell equation describes drug release from a system in which there is a change in surface area and diameter of the particles or tablets Q_0^1/3 - Q^l/3 = k_HCt Where Q_0 is the initial amount of drug, Q is the amount of drug remaining, k_HC is the rate constant, and t is time. The Hixson-Crowell model makes some key assumptions about the matrix and the drug in order to create a simple model. Identify at least two of these assumptions. Explain how experimental data can be used to determine the rate constant k_HC in the Hixson-Crowell model. What does the Hixson-Crowell model tell you about the rate of drug release over time? In other words, what is dQ/dt? Does this make intuitive sense? If your goal is to achieve a constant rate of drug release over time, should you use a surface eroding matrix for drug delivery? Why or why not?

Solution

a) Key assumptions are :

    Drug powder having uniformed size particles, Hixson and Crowell derived the equation which expresses rate of dissolution based on cube root of weight of particles and the radius of particle is not assumed to be constant.

It is assumed that the dissolution occurs in planes which are parallel to the drug surface if the tablet dimensions diminish proportionally, in such a way that the initial geometrical form keeps constant all the time.

b) Experimentally one can fix the initial amount Q_o   and then measure the amount of drug Q in the system at regular intervals of time. Plotting Q_o ^1/3 - Q ^ 1/3 against time will give you a straight line, the slope of which will give K_hc .

c) -1/3 * Q^(-2/3) * dQ / dt = K_HC

       dQ / dt   = - 3 * K_HC * Q^(2/3)

      it shows the rate of change of the amout of drug present in the system is directly proportional to the amount of drug present it the system . Yes the model is intuitive.

d) No you should not use a surface eroding matrix for drug delivery because in this case dQ / dt is not constant.