KINETIC BASIS OF THE NEED FOR PENETRATION ENHANCEMENT

II. KINETIC BASIS OF THE NEED FOR PENETRATION ENHANCEMENT

The simplest model for ocular pharmacokinetics is shown in Figure 1 (5). It is well known that for most drugs the true absorption rate constant is much smaller than the elimination rate constant. This will normally give rise to a flip-flop model. However, when the parallel elimination pathway is intro- duced (Fig. 2) (5), the apparent absorption rate constant is defined as:

Apparent k abs ¼k abs þk loss;pp Thus, the model is not a flip-flop model and drug concentration can be

described as

ð1Þ where F is the fraction of dose absorbed, D is the dose, k and K are

C ¼ ðFD=V d Þ

absorption and elimination rate constants, respectively, and V d is the appar- ent volume of distribution. Obviously, K ¼ k elim ,k¼k abs þk loss;pp : For many drugs, k loss; pp is of the order of 0.5–0.7 min , being several orders of magnitude larger than k abs , which is typically of the order of 0.001 min . As a result, the peak time, which is controlled by k loss;pp and k abs , is similar (20–40 min) for a wide range of compounds since k loss;pp , which is mainly due to drainage, induced lacrimination, etc., predominates over k abs in controlling the peak time.

In order to improve the bioavailability ðF ¼ k abs = ½k abs þk loss;pp nificantly, it is essential to increase k abs by one or two order of magnitudes or reduce k loss;pp to a similar extent.

Several approaches have attempted to reduce the magnitude of k loss;pp . However, it has its limit. Keister et al. (6) showed that reducing the dose volume from 25 mL to zero brings only a fourfold improvement in bioavail- ability for a poorly permeable compound. However, it is practically impos-

Figure 1 A one-compartment model for ocular absorption.

Ocular Penetration Enhancers 283

Figure 2 A two-compartmental model for ocular absorption. sible to have zero dosing volume. Therefore, small dose volumes will give an

improvement in bioavailability that is less than fourfold. Similarly, theoret- ical calculations showed that use of bioadhesives does not necessarily give any benefit if the cornea is poorly permeable to that compound (7). These calculations are as follows: steady-state, at which the rates of delivery and elimination are equal, is approached after about five drug half-lives, and the amount of the drug in a particular ocular compartment can be expressed as

where A is the amount of the drug (in mg), R is the rate of drug input, and K is the elimination rate constant. At steady state, dA=dt ¼ 0, leading to

A SS ¼ R=K ¼ M p t 1=2 = 0:693T where M p is the mass penetrating and t 1=2 is the half-life of the drug. It is

clearly shown that prolonging the contact time ðT Þ via the use of bioadhe- sives will lower A SS provided that M p and t 1=2 are kept constant. For drugs where permeability is not a problem, the use of bioadhesives is beneficial since the therapeutic drug level can be sustained. On the contrary, for a poorly permeable compound, the use of adhesives may lower A SS below the therapeutic level. In order to bring A SS back to a therapeutic level, M p has to

be increased. This requires the use of penetration enhancers. Methods of penetration enhancement such as prodrugs, ion pairing, etc. are beyond the scope of this chapter and will not be discussed. The main focus of this chapter will be ocular penetration enhancers.