The pharmacokinetics of a drug can be mathematically modeled using a technique called compartmental analysis to develop descriptive and predictive information about a drug's concentration at different times in different locations.4 A compartment is an anatomic or physiologic space within an organ that is separated by a barrier to drug transfer (figure 1.1). The drug is assumed to be homogeneously distributed within a compartment, and exchange of the drug between adjacent compartments occurs at a transfer rate determined by the prevailing biochemical and physiologic conditions. This transfer rate is the coefficient describing the change in drug concentration over time in reference to a specific compartment.
From the standpoint of the body as a whole, the eye is a component of the systemic compartment, which is composed of multiple subcompartments, such as tears, cornea, aqueous, iris, ciliary body, vitreous, sclera, retina, and lens. Often, the first pharmacokinetic information obtained for a drug is the corneal permeability coefficient, which is the corneal flux divided by the product of the initial drug concentration times the corneal surface area.5 Usually, this information can be obtained in vitro using Ussing-type chambers.6 The usual values obtained for a large number of compounds used in ophthalmology range from 0.44 x 10-6 to 78.8 x 10-6cm/sec.
Values smaller than 10 x 10-6cm/sec indicate poor penetration.7 Low corneal permeability may be compensated to some degree by higher potency or the introduction of functional groups into the chemical structure to alter the permeability coefficient.
Ocular bioavailability concerns the amount of drug absorbed compared to the amount of drug administered. Drug molecules pass between compartments by either diffusion or active transport processes. Diffusion of a drug follows its concentration gradient and is related inversely to molecular size and directly to the temperature. Active and passive drug transport depends on the chemical structure and molecular configuration of the drug and is affected by competition of other substances for the same transport system. Permeability coefficients for drugs are determined by measuring the drug concentration in compartments at various times.8 The cornea and anterior chamber have important roles in the distribution of drugs within the eye. Coefficients for the transfer of drugs are usually determined between the cornea and aqueous, the removal of drug from the anterior chamber to the blood, the loss of drug within the tears, and the entry of drug from the plasma into the anterior chamber. These transfer coefficients can be used to compare drugs and to gain a better understanding of the importance of each transfer process in the overall phar-macokinetic behavior of the drug.4
1.1.1 Drug Transfer Rate and Concentration. The rates of the pharmacokinetic processes can be characterized as a function of the drug concentration. Many drug transfer processes follow first-order kinetics, in which the rate constant of transfer is proportional to the drug concentration, and the drug half-life (t1/2) is a constant time regardless of the amount of drug administered.9 In a first-order kinetic process, the drug concentration decreases exponentially with time, and on the curvilinear plot of concentration versus time, the concentration asymptotically approaches some final value as time advances toward infinity. The plot of the log drug concentration versus time is linear, and the drug concentration decreases by one-half over each time interval corresponding to the half-life (figure 1.2). Commonly used ophthalmic drug formulations, such as solutions, gels, suspensions, and ointments, deliver drugs at rates that follow first-order kinetics.
A zero-order kinetic rate is not proportional to the drug concentration but is related to some functional capacity involved in the transfer of drug. Active drug transport systems change drug kinetics from first to zero order when the transfer capacity is fully saturated; a higher concentration of the drug will not increase the transfer rate. Normally, it is free drug that diffuses between compartments. Drugs bound to tissue proteins or melanin must be free from their binding sites before the molecules can diffuse into adjacent compartments. Pharmacologic response correlates best with the concentration of free drug at the site of action.3 Zero-order kinetic delivery of a drug to the eye results if a constant concentration of the drug is maintained in the precorneal tear film, creating a steady-state concentration in the tissues, such as with the use of pilocarpine Ocuserts.
1.1.2 Drug Absorption. Ocular absorption of a drug begins when a medication is instilled topically into the cul-de-sac. The drug solution then mixes with the tears to give some unknown dilution. The efficiency of ocular absorption depends on the
Figure 1.2. Pharmacokinetics: semilogarithmic plot of concentration versus time.
Figure 1.2. Pharmacokinetics: semilogarithmic plot of concentration versus time.
adequate mixing of drug with the precorneal tear film and the residence time of drug in the precorneal area.4
A relatively stagnant precorneal tear film layer has a thickness of about 7-9 mm and is composed of mucin, water, and oil.10 Eyelid blinking facilitates the mixing of the drug with the precorneal tear film. A gradient of drug concentration between the precorneal tear film and the cornea and bulbar conjunctival epithelia acts as a driving force for passive drug diffusion into the cornea and conjunctiva.7 The lag time is the time between the instillation of drug and its appearance in aqueous, which reflects the rate of drug diffusion across the cornea.
The amount of drug penetrating the eye is linearly related to its concentration in the tears, unless the drug interacts or binds with other molecules present in the cornea or the cornea becomes saturated because of limited drug solubility. The rate of drug concentration decline in the tears is proportional to the amount of drug remaining in the tears at the time and approximates first-order kinetics. This rate of decline depends on the rate of dilution by fresh tears and the drainage rate of tears into the cul-de-sac.11,12
In normal humans, the basal rate of tear flow is approximately 1 mL/min, and the physiologic turnover rate is approximately 10% to 15% per minute, which decreases with age. Basal tear flow is usually lower in patients with keratoconjunctivitis sicca and slightly higher in contact lens wearers.13 The half-life of the exponential decline of fluorescence in the precorneal tear film in normal humans, as measured by fluo-rophotometry, varies between 2 and 20 minutes. This variability also applies to other substances. The loss rate constant for fluorescein varies depending on the amount of tearing. Reflex tearing caused by stinging from instillation of an irritating drug produces a higher loss rate. Lid closure and local or general anesthesia can decrease the tear flow rate. Physical, psychological, and emotional factors can increase tearing.
Blinking movements force part of the instilled volume through the puncta into the nasolacrimal duct. Each blink eliminates 2 mL of fluid from the cul-de-sac.4 Aside from elimination by drainage through the nasolacrimal route, evaporation of tears, and deposition of drug on lid margins, drug may be bound to proteins in tears and metabolized by enzymes in tears and tissue.14 These processes tend to limit the amount of drug entering the eye. As a result of limited residence time in the pre-corneal area imposed by these factors, but mainly because of rapid drainage, only a small fraction of the dose (1% to 10%) reaches the internal structures. This fraction may be increased by prolonging the residence time at the absorptive surfaces and enhancing the penetration rate through the corneal epithelium, by making the molecule more lipophilic. Transcorneal movement can be increased by changing the barrier properties of the corneal epithelium, by applying an anesthetic, by preservatives in topical medications, or after damaging the epithelium. Conversion of epinephrine to its dipivalyl ester derivative increases its lipophilicity and serves as a prodrug to increase penetration through the epithelium.
The distribution of drugs within the eye depends on many factors. The eye is relatively isolated from the systemic circulation by the blood-retina, blood-vitreous, and blood-aqueous barriers. These barriers comprise the tight junctions between the capillary endothelial cells in the retina and iris, between the nonpigmented ciliary epithelial cells, and between the retinal pigment epithelial cells.15 These tight junctions exclude large molecules such as plasma proteins from entering the eye from the blood circulation, but allow many smaller molecules (molecular weight <500 dal-tons) and drugs to pass. The blood-aqueous barrier is evidenced by the low concentration of proteins in the aqueous and the failure of intravenously injected fluo-rescein to enter the aqueous unless the eye is inflamed. Many drugs in the blood circulation are unable to enter the eye because of these blood-ocular barriers.
The fraction of a topical drug that is absorbed by the eye can enter the systemic blood circulation by at least two pathways:
1. Along with the bulk flow of aqueous by way of the conventional outflow pathways of trabecular meshwork, Schlemm's canal, aqueous collecting channels, and episcleral venous plexus
2. By being absorbed into the blood vessels of the uvea, choroid, and retina
A drug in the aqueous that leaves through the uveoscleral outflow pathway through the iris base and ciliary body may be reabsorbed into the choroidal vessels from the suprachoroidal space.
Drug loss from the precorneal area limits the time available for absorption into the eye. The time to peak drug levels in the eye is determined by the residence time in the precorneal area.16 Most drugs delivered topically to the eye exhibit similar apparent times to peak concentrations in aqueous as the drug drains out of the cul-de-sac within the first 5 minutes. The time it takes for most drugs to reach their peak concentrations in the aqueous is within a rather narrow range of 20-60 minutes.17 Within the cornea, drug may diffuse laterally to the limbus and enter the eye at the iris root. Drugs may also be absorbed from the cul-de-sac across the conjunctiva and enter the eye through the sclera. The sclera poses less of a barrier to hydrophilic drugs than does the cornea, but both are comparable for lipophilic drugs.8
The main route of drug entry into the anterior chamber is through the cornea. Drugs in the aqueous equilibrate with drugs in the tissues in contact with that fluid. Drugs are not distributed uniformly within the eye; molecules may selectively concentrate in certain parts. Most drugs are eliminated from the anterior chamber by bulk flow of aqueous. Normally, turnover of aqueous in human eyes is rapid, with a half-life of approximately 52 minutes.5 In the case of drugs that decrease the formation of aqueous, their effects on the turnover of aqueous may alter the drug elimination rate to favor a longer duration of action.
The distribution of drugs by diffusion from the anterior chamber to the tissues of the posterior segment is hindered by physical barriers, such as the iris, lens, and ciliary body, as well as by the bulk flow of aqueous anteriorly through the pupil. Most topically applied ophthalmic drugs can reach therapeutic concentrations in the anterior segment tissues but not in the posterior segment tissues. There are significant challenges to the delivery of drugs to the retina by topical administration due to these barriers. Therefore, the most commonly used route of administration to deliver drugs to the retina and vitreous is by intravitreal injection. Also, drug concentrations in the posterior segment of the eye can be measured by obtaining tissue samples, such as vitreous or retinal biopsy specimens. Ultimately, the drug enters various cells and acts on enzymes or receptors. Drug molecules may be bound to proteins or pigment and are unable to act until freed from these binding sites.
The relationship between iris color and ocular drug effects was reported as early as 1929.18 Topically applied mydriatic drugs had a slower onset of action in dark-pigmented irides compared with light-pigmented irides. Onset and duration of drug action after topical application were correlated with the retention of drug in the melanin-containing iris. Binding of the drugs by melanin is a very important factor in the control of drug action in the ocular compartments. Many liposoluble drugs are bound by melanin and slowly released later. Ocular drug response may vary from individual to individual depending on the degree of melanin pigmentation of the iris.
After a drug has been applied, it can be metabolized by enzymes in the tears, adnexa, and ocular tissues.19 A broad range of active enzymes have been reported in eye tissues, including esterases, oxidoreductases, lysosomal enzymes, peptidases, glucuronide and sulfate transferases, glutathione-conjugating enzymes, catechol O-methyltransferase, monoamine oxidase, and corticosteroid beta-hydroxylase. Esterase activity in the cornea is involved in the conversion of ester prodrugs, such as dipivalylepinephrine, to their parent compounds. Cholinesterase inhibitors may interfere with prodrug ester hydrolysis in the eye and modify the drug effect.20
Stereochemical factors may affect drug penetration, metabolism, and receptor interaction. Chiral molecules possess an asymmetric carbon atom in the structure and exist in two enantiomeric forms, dextro (d) and levo (/), which rotate polarized light in opposite directions.21 Well-known chiral molecules are amino acids and the catecholamines epinephrine and norepinephrine. The equal mixture of the two en-antiomers is called a racemate. One of the stereoisomers is generally preferred by the enzyme, the transporter, or the receptor. Naturally occurring /-epinephrine or /-norepinephrine is physiologically more active than the unnatural d-isomer.22
Occasionally, drugs containing chiral centers are available as racemates even though the therapeutic benefit may be derived primarily from one isomer. The less active isomer may compete with a more active isomer for an enzyme, a transport system, or the receptor. The metabolic disposition of the racemic drug may appear highly complex because the ratio of the molecular species, d/l, can change in an unpredictable way. In body fluids, one isomer may be converted to another isomer, leading to a racemization of the drug. Occasionally, the "inactive" isomer may exhibit toxicity. The possible differences in behavior between isomers and racemates should be kept in mind when new medications are investigated clinically.
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