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Higuchi’s Model
Drug release from the matrix device by diffusion has been described by Higuchi’s Diffusion equation
ft = Q = √Dδ/τ  (2C- δCs)Cst

Where, Q = Amount of drug released in time‘t’.
D = Diffusion coefficient of the drug in the matrix.
Cs = Solubility of the drug in the matrix.
δ= Porosity of matrix.
τ= Tortuosity.
t = Time (h).

The equation may be simplified then equation becomes;
ft = Q = KH X t1/2

Where, KH = Higuchi dissolution constant.

When data was plotted according to this equation, i.e., cumulative drug released verses square  root of time, yields a straight line, indicating that the drug was released by diffusion  mechanism.

Peppas Korsmeyer Equation
In 1983 Korsmeyer et al. (Korsmeyer et al, 1983) developed a simple, semi-empiric model, when diffusion is the main drug release mechanism, relating exponentially the drug release to the elapsed time (t). 
At/A= ktn

Where, k = Constant.
n = Release.
t = Time.
At and A= Absolutecumulative amount of drug released at time’t’.

This is used when the release mechanism is not well known or when more than one type of release phenomenon could be involved.

Hixon-Crowell Equation
Drug released from the matrix device by diffusion has been described by Hixon-Crowell diffusion equation;
W01/3 - Wt1/3 = ?t

Where, W0 = Initial amount of drug.
Wt = Remaining amount of drug.
t = Time.
? = Constant (Kappa).

This expression applies to pharmaceutical dosage form such as tablets where the dissolution occurs in planes that are parallel to drug surface if tablet dimensions diminish proportionally in such manner that the initial geometrical form keeps constant all the time.

To achieve controlled drug delivery, it is desirable to have a zero-order drug input. Under steady state, rate in = rate out then
R0 = CssCL

This equation shows that the input rate of a controlled release is determined solely by steady state concentration and plasma clearance, t1/2, a common pharmacokinetic parameter is not directly needed to determine the input rate. However, it does play a role in determining the benefits of formulating a drug into controlled-release dosage form. Usually drugs of t1/2 more than 8 hours are not suitable candidates for controlled or sustained release dosage forms because they do not provide benefits over conventional dosage forms. In addition, t1/2 may be useful in determining the dosing interval of controlled release dosage forms. Similarly, volume of distribution is not major consideration in designing controlled-release delivery systems, although often a larger volume of distribution requires a higher drug load to achieve therapeutic blood level. However, there may not exist a direct correlation between pharmacokinetics and pharmacodynamics of a drug. In other words, it may be difficult to predict the effect of a drug based only on pharmacokinetics data. As a result, a PK/PD model required to obtained a rational design of a controlled-release dosage form. Typically a graded response can be represented by
E= PC + E0

Where, P is the proportionality constant, C is the plasma concentration, and E0 is the base line effect. In some cases, a more satisfactory relationship is obtained by using,
E = P log C + E0

In fact, in most cases, the relationship is much more complex than simple linear one, and sometimes it can be represented only by an expression closely related to enzyme kinetics,
E = E0 + (Emax Cn) / (En50) + Cn

By the above discussion, it can be easily conclude that development of sustained release dosage form which will prolong the drug release leading to minimize the peak and valley effect in plasma and provide patients compliance. The advantages of sustained release tablets or capsules are that they can often be taken less frequently than instant formulations of the same drug and that they keep steadier levels of the drug in the bloodstream. By several approaches the residences time of drug delivery system in the gastrointestinal tract can be prolonged. Difference between controlled release and sustained release is that controlled release is perfectly zero order release that is, the drug releases with time irrespective of concentration. On the other hand, sustained release implies slow release of the drug over time period. It may or may not be controlled release.

We thank our management of K. T. Patil college of Pharmacy, Osmanabad for providing required support for completing this research work successfully.

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