KID N EYf iltra tion

secretion(reab sorp tion )

LIVERm etabolism

excretion

LU N GSexhalation

OTH ER Sm other's m ilk

sw eat, sa liva etc .

Elim inationof chem icals from the body

44 . .EliminationElimination

The parameter most commonly used to describe The parameter most commonly used to describe the rate of elimination of a chemical is the the rate of elimination of a chemical is the half-life. Most toxicokinetic processes are half-life. Most toxicokinetic processes are first-order reactions, first-order reactions, i.e. i.e. the rate at which the the rate at which the process occurs is proportional to the amount of process occurs is proportional to the amount of chemical present. High rates (expressed as chemical present. High rates (expressed as mass/time) occur at high concentrations and mass/time) occur at high concentrations and the rate decreases as the concentration the rate decreases as the concentration decreases; in consequence the decrease is an decreases; in consequence the decrease is an exponential curve.exponential curve.

First order eliminationFirst order elimination First order elimination kinetics are described by the

equation:Ct = C0 * e-kt

Taking the natural logarithm of this equation and plotting it semilogarithmically results in a linear graph with a slope of -k, and a y-intercept of ln C0.

Again, to determine the half-life, ½ C0 is substituted into the equation to give:

½ C0= C0e-kt1/2

Taking natural logs and solving for t1/2: t1/2= 0.693/k

The usual way to analyze exponential changes is The usual way to analyze exponential changes is to use logarithmically transformed data which to use logarithmically transformed data which converts an exponential into a straight line. converts an exponential into a straight line. The slope of the line is the rate constant (The slope of the line is the rate constant (kkelel) )

for the process and the half-life for the process for the process and the half-life for the process is calculated as 0.693/is calculated as 0.693/kkelel. Rate constants and . Rate constants and

half-lives can be determined for absorption, half-lives can be determined for absorption, distribution, and elimination processes.distribution, and elimination processes.

The mechanisms of elimination depend on the The mechanisms of elimination depend on the chemical characteristics of the compound:chemical characteristics of the compound:

volatile chemicals are exhaled,volatile chemicals are exhaled, water-soluble chemicals are eliminated in the water-soluble chemicals are eliminated in the

urineurine lipid-soluble chemicals are eliminated by lipid-soluble chemicals are eliminated by

metabolism to more water-soluble molecules, metabolism to more water-soluble molecules, which are then eliminated in the urine and/or which are then eliminated in the urine and/or bile.bile.

FirstFirst--pass metabolismpass metabolism TheThe firstfirst--pass effectpass effect oror presystemic metabolismpresystemic metabolism) ) is a is a

phenomenon ofphenomenon of drug metabolismdrug metabolism whereby thewhereby the concentrationconcentration of of aa drugdrug is greatly reduced before it reaches the systemic is greatly reduced before it reaches the systemic circulationcirculation. . It is the fraction of lost drug during the process of It is the fraction of lost drug during the process of absorption which is generally related to theabsorption which is generally related to the liverliver and gut walland gut wall. . Notable drugs that experience a significant firstNotable drugs that experience a significant first--pass effect arepass effect are ImipramineImipramine, , PropranololPropranolol, , andand LidocaineLidocaine..

After a drug is swallowed, it is absorbed by theAfter a drug is swallowed, it is absorbed by the digestive digestive systemsystem and enters theand enters the hepatic portal systemhepatic portal system. . It is carried It is carried through thethrough the portal veinportal vein into theinto the liverliver before it reaches the rest before it reaches the rest of the bodyof the body. . The liverThe liver metabolizesmetabolizes many drugs, sometimes to many drugs, sometimes to such an extent that only a small amount of active drug such an extent that only a small amount of active drug emerges from the liver to the rest of theemerges from the liver to the rest of the circulatory systemcirculatory system. .

ThisThis first passfirst pass through the liver thus greatly reduces thethrough the liver thus greatly reduces the bioavailabilitybioavailability of the drugof the drug..

Elimination by the KidneyElimination by the Kidney

Drugs are excreted by the kidneys by 2 processes:Drugs are excreted by the kidneys by 2 processes:1) Passive:1) Passive:- glomerular filtration- glomerular filtration- removes molecules up to size of small proteins- removes molecules up to size of small proteins- therefore, protein bound drugs are poorly filtered- therefore, protein bound drugs are poorly filtered- nonsaturable process- nonsaturable process

2) Active: 2) Active: - tubular reabsorption- tubular reabsorption- saturable process- saturable process

     Metabolism in kidneys is a minor elimination routeMetabolism in kidneys is a minor elimination route

Elimination by the LiverElimination by the Liver

Metabolism - majorMetabolism - major

1) Phase I and II reactions1) Phase I and II reactions2) Function: change a 2) Function: change a

lipid soluble to lipid soluble to more water soluble more water soluble molecule to excrete molecule to excrete in kidneyin kidney

3) Possibility of active metabolites 3) Possibility of active metabolites with with same or different properties as same or different properties as parent parent moleculemolecule

Biliary SecretionBiliary Secretion

EXCRETION BY OTHER ROUTESEXCRETION BY OTHER ROUTES LUNG LUNG - - For gases and volatile liquids by diffusion. For gases and volatile liquids by diffusion.

Excretion rate depends on partial pressure of gas Excretion rate depends on partial pressure of gas and blood/air partition coefficient.and blood/air partition coefficient.

MOTHER’S MILKMOTHER’S MILK

a) By simple diffusion mostly. Milk has a) By simple diffusion mostly. Milk has high lipid high lipid contentcontent and and is more acidic than plasmais more acidic than plasma (traps (traps alkaline fat soluble substances). alkaline fat soluble substances).

b) Important for 2 reasons: transfer to babies, b) Important for 2 reasons: transfer to babies, transfer from animals to humans.transfer from animals to humans.

OTHER SECRETIONS – sweat, saliva, etc.. OTHER SECRETIONS – sweat, saliva, etc.. minor contributionminor contribution

Clearance Clearance (CL)(CL)

A measure of the ability of the body to A measure of the ability of the body to eliminateeliminate the drug/toxin in ml/minthe drug/toxin in ml/min

Defined as the rate of drug concentration Defined as the rate of drug concentration eliminated from the body in mL/mineliminated from the body in mL/min Can be defined for various organs in Can be defined for various organs in

the bodythe body Sum of all routes of eliminationSum of all routes of elimination

CLCLtotaltotal = CL = CLliverliver + CL + CLkidneykidney + CL + CLintestineintestine

The The Clearance (Cl)Clearance (Cl) of a drug is the volume of of a drug is the volume of plasma from which the drug is completely plasma from which the drug is completely removed per unit time. The amount eliminated removed per unit time. The amount eliminated is proportional to the concentration of the drug is proportional to the concentration of the drug in the blood.in the blood.

A clearance of 100 mL/minute of a chemical A clearance of 100 mL/minute of a chemical means that 100 mL of blood/plasma is means that 100 mL of blood/plasma is completely cleared of the compound in each completely cleared of the compound in each minute.minute.

The best measure of the ability of the organs of The best measure of the ability of the organs of elimination to remove the compound from the elimination to remove the compound from the body is the clearance (body is the clearance (CLCL):):

Because the rate of elimination is proportional to the concentration, clearance is a constant for first-order processes and is independent of dose. It can be regarded as the volume of plasma (or blood) cleared of compound within a unit of time (e.g. mL/ min).

Renal clearance depends on the extent of protein binding, tubular Renal clearance depends on the extent of protein binding, tubular secretion (active transport) and passive reabsorption in the secretion (active transport) and passive reabsorption in the renal tubule; it can be measured directly from the renal tubule; it can be measured directly from the concentrations present in plasma and urine:concentrations present in plasma and urine:

CL = rate of elimination/CCL = rate of elimination/Cpp

Rate of elimination = KRate of elimination = Kelel * Dose * Dose

VVdd = Dose/C = Dose/Cpp

Therefore CL = KTherefore CL = Kelel*V*Vdd

The total clearance or plasma clearance (which is the sum of all The total clearance or plasma clearance (which is the sum of all elimination processes, elimination processes, i.e. i.e. renal, metabolic, renal, metabolic, etc.etc.) is possibly ) is possibly the most important toxicokinetic parameter.the most important toxicokinetic parameter.

It is measured from the total amount of compound available for It is measured from the total amount of compound available for removal (removal (i.e. i.e. an intravenous dose) and the total area under the an intravenous dose) and the total area under the plasma concentration–time curve (AUC) extrapolated to plasma concentration–time curve (AUC) extrapolated to infinity.infinity.

Plasma clearance reflects the overall ability of the body to remove permanently the chemical from the plasma. Plasma clearance is the parameter that is altered by factors such as enzyme induction, liver disease, kidney disease, inter-individual or inter-species differences in hepatic enzymes or in some cases organ blood flow.

Once the chemical is in the general circulation, Once the chemical is in the general circulation, the same volume the same volume of plasma will be cleared of chemical per minuteof plasma will be cleared of chemical per minute ( (i.e. i.e. the the clearance value) applies irrespective of the route of delivery of clearance value) applies irrespective of the route of delivery of chemical into the circulation. However, the bioavailability (chemical into the circulation. However, the bioavailability (FF) ) will determine the proportion of the dose reaching the general will determine the proportion of the dose reaching the general circulation. Therefore, bioavailability has to be taken into circulation. Therefore, bioavailability has to be taken into account if clearance is calculated from data from a non-account if clearance is calculated from data from a non-intravenous route (intravenous route (e.g. e.g. oral):oral):

The overall rate of elimination, as indicated by the terminal half-The overall rate of elimination, as indicated by the terminal half-life (life (t t ), is dependent on two physiologically related and ), is dependent on two physiologically related and independent variables: CL=Vindependent variables: CL=Vdd*K*Kelel

where where CL CL is the ability to extract and remove irreversibly the is the ability to extract and remove irreversibly the compound from the general circulation, and compound from the general circulation, and V V the extent to the extent to which the compound has left the general circulation in a which the compound has left the general circulation in a reversible equilibrium with tissues.reversible equilibrium with tissues.

Chemicals that are extremely lipid-soluble and Chemicals that are extremely lipid-soluble and are sequestered in adipose tissue are are sequestered in adipose tissue are eliminated slowly. Lipid soluble eliminated slowly. Lipid soluble organochlorine compounds, which are not organochlorine compounds, which are not substrates for P450 oxidation, due to the substrates for P450 oxidation, due to the blocking of possible sites of oxidation by blocking of possible sites of oxidation by chloro-substituents, are eliminated extremely chloro-substituents, are eliminated extremely slowly: for example, the half-life of 2,3,7,8-slowly: for example, the half-life of 2,3,7,8-tetrachlorodibenzodioxin (TCDD) is about 8 tetrachlorodibenzodioxin (TCDD) is about 8 years in humans.years in humans.

Classical ToxicokineticsClassical Toxicokinetics If we assume that the concentration of a chemical in blood or

plasma is in some describable dynamic equilibrium with its concentrations in tissues, then changes in plasma toxicant concentration should reflect changes in tissue toxicant concentrations and relatively simple kinetic models can adequately describe the behavior of that toxicant in the body system.

Classic toxicokinetic models typically consist of a central compartment representing blood and tissues that the toxicant has ready access and equilibration is achieved almost immediately following its introduction, along with one or more peripheral compartments that represent tissues in slow equilibration with the toxicant in blood.

One-Compartment ModelThe most straightforward toxicokinetic

assessment entails quantification of the blood or more commonly plasma concentrations of a toxicant at several time points after a bolus intravenous (iv) injection. Often, the data obtained fall on a straight line when they are plotted as the logarithms of plasma concentrations versus time; the kinetics of the toxicant is said to conform to a one-compartment model. Mathematically, this means that the decline in plasma concentration over time profile follows a simple exponential pattern as represented by the following mathematical expressions:Ct = C0 × e−kel*t

First order eleminationFirst order elemination First order elimination kinetics are described by the

equation:Ct = C0 * e-kt

Taking the natural logarithm of this equation and plotting it semilogarithmically results in a linear graph with a slope of -k, and a y-intercept of ln C0.

Again, to determine the half-life, ½ C0 is substituted into the equation to give:

½ C0= C0e-kt1/2

Taking natural logs and solving for t1/2: t1/2= 0.693/k

Two compartments modelTwo compartments model

Two-Compartment ModelAfter rapid iv administration of some toxicants, the semi-

logarithmic plot of plasma concentration versus time does not yield a straight line but a curve that implies more than one dispositional phase. In these instances, it takes some time for the toxicant to be taken up into certain tissue groupings, and to then reach an equilibration with the concentration in plasma; hence, a multi-compartmental model is needed for the description of its kinetics in the body.

The concept of tissue groupings with distinct uptake and equilibration rates of toxicant becomes apparent when we consider the factors that govern the uptake of a lipid-soluble, organic toxicant.

Plasma concentration-time profile of a toxicant that exhibits multi-compartmental kinetics can be characterized by multiexponential equations. For example, a two-compartment model can be represented by the following bi-exponential equation.

C = A × e−α×t + B × e−β×t where A and B are coefficients in units of toxicant concentration,

and α and β are the respective exponential constants for the initial and terminal phases in units of reciprocal time. The initial (α) phase is often referred to as the distribution phase, and terminal (β) phase as the post-distributional or elimination phase.

Zero order eliminationZero order elimination

A constant amount of drug is absorbed regardless of dose.

A plot of this equation is linear with a slope, -k, and a y-intercept, C0. The elimination half-life may be calculated from this equation for a drug which exhibits zero order elimination. This occurs when Ct = ½ Co and t = t1/2

Loading Doses

The loading dose is one or a series of doses that are administered at the beginning of therapy.

The objective is to reach the target concentration rapidly. The loading dose can be estimated with the following formula:

Loading Dose = Target Cp x Vss/F

whereCp = Concentration in plasmaVss= Volume of Distribution at steady stateF = Fractional bioavailability of the dose

Dosing Rate

In the majority of clinical situations, drugs are administered as a series of repeated doses or asa continuous infusion in order to maintain a steady state concentration. Therefore, a maintenance dose must be calculated such that the rate of input is equal to the rate of drug loss. This may be determined using the following formula:

Dosing Rate = Target concentration × CL/F

whereCL= ClearanceF= Fractional bioavailability of the dose