The Higuchi Model

Equation (4.2) reveals that the fraction of drug released is linearly related to the square root of time. However, (4.2) cannot be applied throughout the release process since the assumptions used for its derivation are not obviously valid for the entire release course. Additional theoretical evidence for the time limitations in the applicability of (4.2) has been obtained [10] from an exact solution of Fick s second law of diffusion for thin films of thickness S under perfect sink conditions, uniform initial drug concentration with cq cs, and assuming constant diffusion coefficient of drug T in the polymeric film. In fact, the short-time approximation of the exact solution is 

This arbitrary recommendation does not rely on strict theoretical and experimental findings and is based only on the fact that completely different physical conditions have been postulated for the derivation of the equivalent (4.2) and (4.3), while the underlying mechanism in both situations is classical diffusion. In this context, a linear plot of the cumulative amount of drug released q (t) or the fraction of drug released q (f) /f/,Xj (utilizing data up to 60% of the release curve) vs. the square root of time is routinely used in the literature as an indicator for diffusion-controlled drug release from a plethora of delivery systems. 

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The Higuchi model gave the worst fit for the data because of the change of the tablet surface during the dissolution test. With the exception of the formulation obtained by direct compression in a rotary machine, the dissolution profiles were well fitted by the Weibull function. A high density in the centre of the tablets may explain the sigmoid aspect of the dissolution profiles. 

The data were then treated with equation (2), and the cumulative amounts of drug released (0 were plotted against the square root of the time (t1/2) (Fig. 1). Excellent linearity was found, confirming that the release-permeation data followed the Higuchi model. 

The Higuchi model is an approximate solution in that it assumes a pseudosteady state , in which the concentration profile from the dispersed drug front to the outer surface is linear. Paul and McSpadden [24] have shown that the correct expression can be written as ... 

As in the Higuchi model, Fick s first law is applied and the flux J is ... 

The presuppositions for the application of the Higuchi law (4.2) have been discussed in Section 4.1. However, it is routinely quoted in the literature without a rigorous proof that only the first 60% of the release curve data should be utilized for a valid application of (4.2). Recently, this constraint has been verified for the Higuchi model using Monte Carlo computer simulations [82] (cf. Appendix B)-... 

Monolithic Devices—In these systems the drug is homogeneously dispersed within a bioerodible polymer matrix, and release of the drug can be controlled either by diffusion or by polymer erosion. If erosion of the matrix is very much slower than drug diffusion, then release kinetics follow the Higuchi model (37) and drug release rate decreases exponentially with time, following t dependence over a major portion of the release rate. 

Whenever the drug is dispersed in the polymer at low eoncentrations, drug release from a slab geometry may be described using the Higuchi model (a.85-a.87). Thus ... 

In vitro dissolution was virtually complete after 6-8 hr. Since the plot of cumulative drug release versus time is hyperbolic, the authors attempted to fit the data to the Higuchi matrix dissolution model (116,117), which predicts a linear correlation between cumulative drug release and the square root of time. Linearity occurred only between 20 and 70% release. 

The Higuchi-Hiestand model [43] permits the a priori estimation of the mass transport coefficient for the dissolution of finely divided drug particles. The model relates the particle radius, a(t), with time according to... 

Ho, N. F., Higuchi, W. I., Quantitative interpretation of in vivo buccal absorption of n-alkanoic acids by the physical model approach, /. Pharm. Sci. 1971, 60, 537-541. 

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. 

Equation (3.58) and Equation (3.61) are the Hixson and Crowell cube-root and the Higuchi and Hiestand two-thirds-root expressions, respectively. The cube-root and the two-thirds-root expressions are approximate solutions to the diffusional boundary layer model. The cube-root expression is valid for a system where the thickness of the diffusional boundary layer is much less than the particle radius whereas the two-thirds-root expression is useful when the thickness of the boundary layer is much larger than the particle radius. In general, Equation (3.57) is more accurate when the thickness of the boundary layer and the particle size are comparable. 

The Higuchi and Hixson Crowell model as well as the nonlinear regression of Peppas and Peppas-Sahlin were employed to study the release data. Higuchi s slope... 

Special cases of such bilinear models are the McFarland model [McFarland, 1970], where b2 = 2b and p = 1 and the Higuchi-Davis model [Higuchi and Davis, 1970], where 2 = 1 and P = Vup / Vaq, which is the ratio between the volume of the lipid phase Viip and the volume of the aqueous phase Vaq. 

Drug Release Rate Behavior - Desai et al have reported results of extensive studies on the release of drug from matrices. Taking the basic physical model approach and beginning with the Higuchi relationship these authors have quantitatively investigated the influence of many factors upon the rate of release. The equation was also found by Lapidus and Lordi to apply to a system having hydrophillic gum as the matrix. 

According to the general model of Higuchi [64], the quantity of the active substance released (M ) is determined by the surface (A), the diffusion coefficient (D), the initial concentration of the active substance (C ), and the solubility of the active substance (C ) ... 

Higuchi diffusion equation was applied to analyze Na-DFC release from the examined mesophases. Higuchi model implies that dmg release is primarily controlled by diffusion through the matrix and can be described by the following equation ... 

Higuchi model (16) applies and is true up to 60-70% of release, t5q)ically from a sphere or microsphere. The pesticide maybe dissolved or dispersed in the polymer for dissolved pesticide the second phase of release is by first-order kinetics. For dispersed pesticide the t kinetics last for almost all the release. These kinetics are a special case of the generalized description (17) of proportional release (at time t) from matrix or monolithic devices, as follows ... 

We speculated that DT release from the granule was simple diffusion by reason of its formula, so the release profile was analyzed by the Higuchi diffusion model equation (3, 4). The Higuchi diffusion model can be simplified, as in the following equation (3 7). 

The effect of the water temperature on the release rate was analyzed by the Higuchi diffusion model in the same way and the results are shown in Table V. It was revealed that the release rate was affected by the water temperature and agreed with the Higuchi diffusion model at each temperature. 

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