Pk - Principles

Pharmacokinetic Principles

The process of absorption, distribution, metabolism and excretion are often quantitated retrospectively so that dosage regimens that target therapeutic concentrations can be propectively predicted.

The pharmacokinetic characteristics of a particular drug (rates of absorption, distribution, biotransformation, and excretion) determine its concentration in the plasma. Because the intensity of the tissue response is usually determined by the concentration of the drug in the direct environment of the receptors, a drug’s concentration in plasma is generally assumed to be correlated with the time course of its action. Dosage regimens are derived from pharmacokinetic studies in normal animals but often require modification in diseased, young, old, obese, thin, or pregnant animals. A large number of pharmacokinetic measures can be determined from time-course studies of drug concentrations in plasma, but only the more clinically useful features and values are emphasized below.

Quantitation of Drug Absorption: This includes both a rate component and an extent component.

Drug concentration in blood - Drug concentrations in the blood can be determined and graphed against time. In most instances, the time course of a drug’s concentration in the plasma correlates well with the onset, intensity, and duration of the pharmacologic effect. Thus, the measurement of sequential plasma concentration of drugs after their administration is used to establish dosage regimens that are likely to produce the desired therapeutic levels for appropriate periods of time, without the risk of drug failure or toxicity.

           

Single-dose Concentration Curves After Extravascular Administration: When a drug is administered by an extravascular route, it usually appears in the plasma within a short time, and its concentration rises steadily until it peaks. Once absorbed into the circulation, it is subjected simultaneously to distribution, biotransformation, and excretion. During the initial period, the rate of absorption and distribution exceeds the rate of elimination. The peak plasma concentration is reached when absorption and elimination rates are equal. Thereafter, the elimination rate exceeds the rate of absorption because less drug remains available at the site of administration, and plasma drug levels begin to fall.

           

The term “bioavailability” is used to express the rate and extent of absorption of a drug from a dosage form as determined by its concentration-time curve in blood or by its excretion in urine. Bioavailability  (F) is a measure of the fraction of administered dose of a drug that reaches the systemic circulation in the unchanged form. Bioavailability of drug injected i.v. is 100% but is frequently lower after oral ingestion because – 1. the drug may be incompletely absorbed, 2. the absorbed drug may undergo first pass metabolism in intestinal wall / liver or be excreted in bile. Incomplete bioavailability after s.c. or i.m. injection is less common, but may occur due to local binding of the drug.  Bioavailability for orally administered drugs are determined by administering equal doses of a drug by the IV (absorption effectively 100%) and PO routes and then comparing the areas under the 2 curves. Bioavailability is expressed as a percentage. The same principles can be applied to calculation of the bioavailability of drugs administered by other routes.

           

Single-dose Concentration Curves After Intravascular Administration: When a drug is administered by rapid IV injection, the maximum concentration in the blood is reached almost at once and immediately begins to fall. The profile of this decline can be determined by monitoring blood levels at periodic intervals and then plotting these concentrations against time.

           

From the single-dose concentration curves (extravascular and intravascular), a number of pharmacokinetic parameters can be calculated. These include the transfer rate constants between central and peripheral compartments; the elimination rate constant ( K_el ) for disappearance of drug from the central compartment; and the elimination half-life ( t½ ), which has important clinical significance when determining dosing interval.

Quantitating Drug distribution: Just as with drug absorption, the distribution of drugs in the animal can be quantified interms of rate and extent of distribution by evaluation of plasma concentrations over time.

Rate of distribution: Plasma concentrations decline very rapidly shortly after administration of an i.v. dose. The rate of that decline is dependent upon the ability of the drug to distribute from the blood stream into extracellular fluids and tissues. The rate of distribution can be described as half-life of distribution, interpreted as the time it takes for 50% of the drug in the plasma to distribute outside of the blood stream.

Extent of distribution: The Extent of distribution is described in terms of volumes of hypothetical fluid compartments, with larger volumes of distribution reflecting more extensive distribution from plasma into tissues. 

Appraent Volume of Distribution - The pharmacokinetic measure used to indicate the pattern of distribution of a drug in plasma and in the different tissues, as well as the size of the compartment into which a drug would seem to have distributed in relation to its concentration in plasma, is known as the apparent volume of distribution (Vd). It is usually reported as liters (L) or as liters per kilogram (L/kg) if corrected for the body weight of the animal. The apparent Vd for a drug is determined by its degree of water or lipid solubility, the extent of plasma- and tissue-protein binding, and the perfusion of tissues. Drugs that tend to maintain high concentrations in the plasma because of low lipid solubility, extensive binding to plasma proteins, and diminished tissue binding have low Vd. The reverse is true for drugs with high apparent Vd. The value of Vd is characteristic for a drug and is usually constant over a wide dose range for a given species of animal. However, a number of clinically significant factors can influence the Vd. Included among these are age; functional status of the kidneys, liver, and heart; fluid accumulations; concentration of plasma proteins; acid-base status; inflammatory processes or necrosis; and any other causes for alteration in the degree of plasma-protein binding. Vd is used to determine dose. A dose necessary to achieve desired plasma concentration can be calculated from the formula D = C × Vd × body wt (in kg), in which D is the dose and C is the required plasma concentration for a given drug.

Drug Clearance - Once a drug is absorbed and distributed among the tissues and body fluids, it is then eliminated, or cleared, mainly by the liver and kidneys. Consequently, the plasma concentration of a drug decreases steadily, although at different rates for various drugs in different species. After a single dose, only ~3% of a given dose remains in the body after 5 half-lives because 96.87% has been cleared by this time. Drug clearance (Cl) is defined as the volume of plasma that would contain the amount of drug excreted per minute or, alternatively, the volume of plasma that would have to lose all of the drug that it contains within a unit of time (usually 1 min) to account for an observed rate of drug elimination. Thus, clearance expresses the rate or efficiency of drug removal from the plasma but not the amount of drug eliminated. The concept of drug clearance is of great clinical significance.

           

Renal clearance is defined as the volume of plasma from which the drug is completely cleared in unit time. The renal clearance of drugs depends on urine pH, extent of plasma-protein binding, and renal plasma flow. These factors may vary from animal to animal as well as among species, because of differences in diet, environmental temperature, physical activity, disease, and concomitant use of certain drugs. For drugs that are excreted primarily by glomerular filtration, the animal’s creatinine clearance may serve as an indicator of drug clearance because creatinine undergoes complete glomerular filtration while being subjected to minimal tubular reabsorption. Consequently, creatinine clearance rate can be used for adjusting dosage schedules of some drugs in animals with impaired renal function.

            Kinetics of elimination: This provides the basis for, as well as serves to devise rational dosage regimens and to modify them according to individual needs. There are 3 fundamental pharmacokinetic parameters, viz., bioavailability (F), volume of distribution (V) and clearance (CL) which must be understood. The first two have already been considered.

            Drug elimination is the sum total of metabolic inactivation and excretion. Drug is eliminated only from the central compartment (blood) which is in equilibrium with peripheral compartments including the site of action. Depending upon the ability of the body to eliminate a drug, certain fraction of the central compartment may be considered to be totally ‘cleared’ of that drug in a given period of time to account for elimination over that period.

            Clearance of a drug is the theoretical volume of plasma from which the drug is completely removed in unit time. It can be calculated as

            CL = Rate of elimination / C, where C is the plasma concentration.

            For majority of drugs the processes involved in elimination are not saturated over the clinically obtained concentrations, they follow

            First order (Exponential) kinetics – The rate of elimination is directly proportional to drug concentration, CL remains constant; or a constant fraction of the drug present in the body is eliminated in unit time.

            Few drugs, however, saturate eliminating mechanisms and are handled by,

            Zero order (Linear) Kinetics – The rate of elimination remains constant irrespective of drug concentration, CL decreases with increase in concentration; or a constant amount of the drug is eliminated in unit time, e.g., ethyl alcohol.

            The elimination of some drugs approaches saturation over the therapeutic range, kinetics changes from first order to zero order at higher doses. As a result plasma concentration increases disproportionately with increase in dose. E.g., pheytoin, tolbutamide, theophyline, warfarin.

            Plasma half life of a drug is the time taken for its plasma concentration to be reduced to half of its original value. Mathematically elimination t ½ is t ½ = ln2/k, where ln2 is the natural logarithm of 2 (or 0.693) and k is the elimination rate constant of the drug, i.e., the fraction of the total amount drug in the body which is removed per unit time.

            For example, if 2g of the drug is present in the body and 0.1g is eliminated every hour, then k = 0.1/2 = 0.05. It is calculated as k = CL / V. Therefore t ½ = 0.693 x V/CL.

            As such, half-life is a derived parameter from two variables, V and CL both of which may change independently. It, therefore, is not an exact index of drug elimination. Nevertheless, it is a simple and useful guide to the sojourn of the drug in the body, i.e., after

            1 t ½ - 50% drug is eliminated.

            2 t ½ - 75% (50 +25) drug is eliminated.

            3 t ½ - 87.5 (50 +25 +12.5) drug is eliminated.

            4 t ½ - 93.75 (50 + 25 + 12.5 + 6.25) drug is eliminated.

Thus, nearly complete drug elimination occurs in 4 – 5 half lives.

For drugs eliminated by first order kinetics – t ½ remains constant because V and CL do not change with dose; Zero order kinetics – t ½ increases with dose because CL progressively decreases as dose is increased.      

           

Hepatic clearance is defined as the volume of plasma that is totally cleared of drug in 1 min during passage through the liver. Most drugs, except highly hydrophilic compounds, are cleared from the plasma mainly by biotransformation in the liver, although biliary excretion can also contribute to the hepatic clearance of a drug. The main factors that determine hepatic clearance include hepatic blood flow (delivery of drug to the liver), uptake of the unbound drug by the hepatocytes from the blood, metabolic transformation of the drug by microsomal or other enzyme systems, and rate of biliary secretion.

           

Some drugs undergo substantial removal from the portal circulation by the liver after administration PO. This “first-pass” effect can significantly reduce the amount of parent drug that reaches the systemic circulation. A number of factors can modify the magnitude of the first-pass effect for a particular drug. Hepatic clearance can be impaired by liver disease, biliary stasis, decreased hepatic blood flow, and drugs that inhibit microsomal enzyme systems. Microsomal enzyme inducers often increase hepatic clearance of a concurrently administered drug. There is no reliable liver function test to assess the impediment of hepatic clearance of drugs (as creatinine clearance does for the kidneys). The dose rates for drugs used in animals with liver disease must be adjusted on clinical judgment alone.

           

Steady State Plasma Concentration (Repeated Administration or Constant IV Infusion): In some cases, the desired therapeutic effect of a drug is produced with a single dose. However, to achieve a satisfactory response, it is frequently necessary to maintain drug concentrations in the therapeutic range for a longer time. Rather than administering large doses, which could be potentially toxic, repeated safe doses at regular intervals or continuous IV delivery are generally necessary.

           

When a drug is infused IV, the plasma concentration continues to rise until elimination equals the rate of delivery into the body. Regardless of the drug, 50% of the plateau concentration is attained in 1 half-life of the drug; for 2, 3, and 4 half-lives, 75%, 87.6%, and 93.6% of the plateau concentration are reached, respectively. For practical purposes, steady state is achieved by 3-5 half-lives. The time required to reach steady state depends only on the drug’s half-life. The shorter the half-life, the more rapidly steady state is reached. The size of the dose and the route of administration have little effect. Consequently, whether a drug is delivered by constant or intermittent IV injection, by other parenteral routes (provided there is no pharmaceutical manipulation to delay absorption), or PO, a steady state concentration is reached after at least 5 half-lives. The magnitude of drug concentrations at steady state compared with the first dose is determined by the relationship between dosing interval and the half-life. For drugs with a long half-life compared with the dosing interval, the drug will markedly accumulate. For drugs with a short half-life compared with the dosing interval, most of the drug is eliminated between doses, with little accumulation.

           

A drug normally requires some time to reach steady state. When some haste is necessary, plasma levels may be achieved more rapidly by the administration of a loading dose or doses. This entails the administration of a single large dose or smaller doses at frequent intervals to bring the concentration in plasma quickly to the level desired during the steady state. The loading dose required to achieve the plasma levels present at steady state can be determined from the fraction of drug eliminated during the dosing interval and the maintenance dose.

           

An appropriate dosing interval for most drugs depends on the distance between the maximum and the minimum target drug concentration (i.e., therapeutic range). Shorter dosing intervals compared with half-life increase the risk of drug-induced toxicity because of increased blood levels. Prolonged dosing intervals diminish the drug’s efficacy because of decreased blood levels. Often, however, dosing intervals equal to the half-lives are impractical for drugs with short half-lives. In most cases, either high doses of a relatively nontoxic drug are given to attain therapeutic concentrations for a sufficient time period, or potentially harmful drugs are administered by careful IV infusion. Another approach is to use dosage formulations or devices that allow for a more gradual release of the active principle into the systemic circulation.

            Plateau principle – When constant dose of a drug is repeated before the expiry 4 t ½ , it would achieve higher peak concentration, because some remnant of the previous dose will be present in the body. This continues with every dose until progressively increasing rate of elimination (which increases with increase in concentration) balances the amount administered over the dose interval. Subsequently plasma concentration plateaus and fluctuates about an average steady state level. This is known as plateau principle of the drug accumulation. Steady state is achieved in 4 –5 half lives unless dose interval is very much longer than t ½. The amplitude of fluctuations in plasma concentration at steady state depends on the dose interval relative to t ½ i.e., the difference between the maximum and minimum levels is less if smaller doses are repeated more frequently (dose rate remaining constant). Dose intervals are generally a compromise between what amplitude of fluctuations is clinically tolerated (Loss of efficacy at troughs and side effects at peaks) and what frequency of dosing is convenient. However,if the dose rate is changed, a new average Cpss is attained over next 4 –5 half lives. When the drug is administered orally (absorption takes some time), average Cpss is approximately 1/3 of the way between the minimal and maximal levels in s doseinterval.

Target level strategy – For drugs whose effects are not easily quantifiable and safety margin is not big (e.g., anticonvulsants, antidepressants, lithium, antiarrhythmics, theophylline, some anti microbials, etc.), or those given to prevent the event, it is best to aim at achieving a certain plasma concentration which has been defined to be in the therapeutic range; such data are now available for most drugs of this type.

            Drugs with short t ½ (up to 2–3 hr) administered at conventional intervals (6-12hrs) achieve the target levels only intermittently and fluctuations in plasma concentration are marked. For drugs with longer t ½ a dose that is sufficient to attain the target concentration after single administration, if repeated will accumulate according to plateu principle and produce toxicity later on. On other hand, if the dosing is such as to attain target level at steady state, the therapeutic effect will be delayed by about 4 half lives. Such drugs are often administered by initial loading and subsequent maintenance doses.

            Loading dose – is a single or few quickly repeated doses given in the beginning to attain target concentration rapidly. It maybe calculated as Loading Dose = target Cp x V / F. Thus, loading dose is governed only by V and not CL or t ½.

            Maintenance dose – is one that is to be repeated at specified intervals after the attainment of target Cpss so as to maintain the same by balancing elimination. The maintenance dose rate is computed by equation dose rate = target Cpss x CL / F and is governed by CL (or t½) of the drug.