Higuchi equation

Goodness-of-fit analysis applied to release data showed that the release mechanism was described by the Higuchi diffusion-controlled model. Confirmation of the diffusion process is provided by the logarithmic form of an empirical equation (Mt/ M=ktn) given by Peppas. Positive deviations from the Higuchi equation might be due to air entrapped in the matrix and for hydrophilic matrices due to the erosion of the gel layer. Analysis of in vitro release indicated that the most suitable matrices were methylcellulose and glycerol palmitostearate. 

As the concentration of polyvinyl chloride and glycerol palmitostearate was increased between 15% and 20%, a non-significant decrease in released amount was obtained, while a slight difference in the amount released was observed beween 10% and 15% of polymer concentration (Table 4). Deviations from the Higuchi equation were observed (Table 3). These positive deviations might be due to the air entrapped in the matrix. Similar results were also obtained with polyvinyl chloride by Desai et al. [14] and Korsmeyer etal. [15]. 

To analyse the in vitro data in terms of more meaningful parameters, the data were first treated with a simplified Higuchi equation [22] ... 

The drug release profile was plotted against time (Figs. 4 and 5) and it was observed that the release kinetics followed both first-order and Higuchi equations up to 75-80% of the cumulative drug release. The micromatrices followed the Higuchi equation (NONLIN package). 

The permeability of a number of gases through acrylonitrile-vinyl acetate (PAN-PVAc) and acrylonitrile-styrene (PAN-PS) copolymers has been studied over a wide range of composition Calculations on the basis of Eq. (30), or of the (empirical) Higuchi equation 100)... 

The presence of insoluble ingredients in the formulations helps to maintain the physical dimension of a hydrophobic matrix during drug release. As such, diffusion of the active form from the system is the release mechanism, and the corresponding release characteristic can be described by the Higuchi equation (Eq. 4.11). Very often, pores form within a hydrophobic matrix as a result of the release of the active ingredient. For a porous monolithic system, Eq. (4.11) can be further modified as18... 

Figure 4.5 Log-log plot of 1—n (t) /no vs. time. Simulation results are indicated as points using the first 60% of the release data. The slope of the fitted line is 0.51 and corresponds to the exponent of the Higuchi equation. The theoretical prediction is 0.50.

In a matrix tablet, the following Higuchi equations are given depending on the polymeric structures of the homogenous and porous matrix [20] ... 

For systems where drug release involves the dissolution of a soluble drug at high concentrations from an insoluble matrix, the Higuchi equation adequately describes release rates [Eq. (3)]. 

Figure 3 Scheme of the pseudo-steady-state approach, which is used for the derivation of the classical Higuchi equation. Assumed drug concentration-distance profiles in a thin ointment film initially containing a significant drug excess and in contact with a perfect sink. 

Figure 12.27. Comparison of (O) theoretically predicted diffusion curve based on Higuchi-Higuchi equation (12.40) with ( ) experimental results for oxygen permeation through poly(vinyl acetate) containing 0.28 volume fraction of polystyrene latex particles. (Peterson, 1968.)...

The complete Higuchi-Higuchi equation gives a still somewhat lower bound to the permeability, but, at least for the limited evidence available so far (Manson and Chiu, 1973aX still seems to overpredict permeability, at least in the case of a glass-sphere-filled epoxy resin. 

Higuchi equation, amount released per surface area, Q, versus square root of time, t, should yield a straight line. 

The Higuchi equation (Eq. 22) has been applied to systems in which the initial protein concentration per unit volume (A) is above its solubility in that hydrogel matrix, c as found in a reservoir system. 

J. Siepmann, and N.A. Peppas, Higuchi equation Derivation, apphcations, use and misuse,... 

The effect of the amount of the wax or ASD was analyzed by the Higuchi diffusion model equation. The result was that the release rate varied depending on the amount of these ingredients and agreed with the Higuchi equation. Then, the release rate coefficient, k, was plotted against the amount of the wax or ASD and linear relationships were obtained as shown in Figure 7 and 8. 

There is a maximum amount of internal phase that can be accommodated before these monolithic [FUPC] systems fail to obey the Higuchi equation. Figure 5 suggests that this limit is reached at about 25% 5-fluorouracil. At about this level of internal phase, discontinuities develop within the sample which lead to pockets of 5-FU rather than a uniform distribution of this material throughout the poly(caprolactone). Even though the samples appear homogeneous on visual inspection, the data indicate that they lack true homogeneity. 

The data for the copolymer systems and the 25 75 [FUPC] samples is plotted according to the Higuchi equation in Figure 8. Although the [FUPC] sample approximates a straight line, neither the powdered nor the pellet form of the EMCF MMA 50 50 copolymer shows such behavior. On the contrary, both copolymer samples exhibit an S-shaped curve. If a zero-order system is plotted against the square root of time, the resultant... 

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