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Elimination
of chemicals from the body
KIDNEY
LIVER
filtration
secretion
metabolism
excretion
(reabsorption)
LUNGS
OTHERS
exhalation
mother's milk
sweat, saliva etc.
4. Elimination
The parameter most commonly used to describe
the rate of elimination of a chemical is the
half-life. Most toxicokinetic processes are
first-order reactions, i.e. the rate at which the
process occurs is proportional to the amount of
chemical present. High rates (expressed as
mass/time) occur at high concentrations and
the rate decreases as the concentration
decreases; in consequence the decrease is an
exponential curve.
First 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
to use logarithmically transformed data which
converts an exponential into a straight line.
The slope of the line is the rate constant (kel)
for the process and the half-life for the process
is calculated as 0.693/kel. Rate constants and
half-lives can be determined for absorption,
distribution, and elimination processes.
The mechanisms of elimination depend on the
chemical characteristics of the compound:
 volatile chemicals are exhaled,
 water-soluble chemicals are eliminated in the
urine
 lipid-soluble chemicals are eliminated by
metabolism to more water-soluble molecules,
which are then eliminated in the urine and/or
bile.
First-pass metabolism
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The first-pass effect or presystemic metabolism )is a
phenomenon of drug metabolism whereby the concentration of
a drug is greatly reduced before it reaches the systemic
circulation. It is the fraction of lost drug during the process of
absorption which is generally related to the liver and gut wall.
Notable drugs that experience a significant first-pass effect
are Imipramine ,Propranolol ,and Lidocaine.
After a drug is swallowed, it is absorbed by the digestive
system and enters the hepatic portal system .It is carried
through the portal vein into the liver before it reaches the rest
of the body. The liver metabolizes many drugs, sometimes to
such an extent that only a small amount of active drug emerges
from the liver to the rest of the circulatory system .
This first pass through the liver thus greatly reduces the
bioavailability of the drug.
Elimination by the Kidney
Drugs are excreted by the kidneys by 2 processes:
1) Passive:
- glomerular filtration
- removes molecules up to size of small proteins
- therefore, protein bound drugs are poorly filtered
- nonsaturable process
2) Active:
- tubular reabsorption
- saturable process
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Metabolism in kidneys is a minor elimination route
Elimination by the Liver
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Metabolism - major
1) Phase I and II reactions
2) Function: change a lipid soluble to
more water soluble molecule to excrete
in kidney
3) Possibility of active metabolites with
same or different properties as parent
molecule
Biliary Secretion
EXCRETION BY OTHER ROUTES

LUNG - For gases and volatile liquids by
diffusion.
Excretion rate depends on partial pressure of gas
and blood/air partition coefficient.

MOTHER’S MILK
a) By simple diffusion mostly. Milk has high lipid
content and is more acidic than plasma (traps
alkaline fat soluble substances).
b) Important for 2 reasons: transfer to babies,
transfer from animals to humans.

OTHER SECRETIONS – sweat, saliva, etc..
minor contribution
Clearance (CL)
A measure of the ability of the body to
eliminate the drug/toxin in ml/min
Defined as the rate of drug concentration
eliminated from the body in mL/min

Can be defined for various organs in the
body

Sum of all routes of elimination

CLtotal = CLliver + CLkidney + CLintestine
The Clearance (Cl) of a drug is the volume of
plasma from which the drug is completely
removed per unit time. The amount eliminated
is proportional to the concentration of the drug
in the blood.
 A clearance of 100 mL/minute of a chemical
means that 100 mL of blood/plasma is
completely cleared of the compound in each
minute.
The best measure of the ability of the organs of
elimination to remove the compound from the
body is the clearance (CL):
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
secretion (active transport) and passive reabsorption in the
renal tubule; it can be measured directly from the
concentrations present in plasma and urine:
CL = rate of elimination/Cp
Rate of elimination = Kel * Dose
Vd = Dose/Cp
Therefore CL = Kel*Vd
The total clearance or plasma clearance (which is the sum of all
elimination processes, i.e. renal, metabolic, etc.) is possibly
the most important toxicokinetic parameter.
It is measured from the total amount of compound available for
removal (i.e. an intravenous dose) and the total area under the
plasma concentration–time curve (AUC) extrapolated to
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 interspecies differences in hepatic enzymes or in some
cases organ blood flow.
Once the chemical is in the general circulation, the same volume
of plasma will be cleared of chemical per minute (i.e. the
clearance value) applies irrespective of the route of delivery of
chemical into the circulation. However, the bioavailability (F)
will determine the proportion of the dose reaching the general
circulation. Therefore, bioavailability has to be taken into
account if clearance is calculated from data from a nonintravenous route (e.g. oral):
The overall rate of elimination, as indicated by the terminal halflife (t ), is dependent on two physiologically related and
independent variables: CL=Vd*Kel
where CL is the ability to extract and remove irreversibly the
compound from the general circulation, and V the extent to
which the compound has left the general circulation in a
reversible equilibrium with tissues.
Chemicals that are extremely lipid-soluble and
are sequestered in adipose tissue are
eliminated slowly. Lipid soluble
organochlorine compounds, which are not
substrates for P450 oxidation, due to the
blocking of possible sites of oxidation by
chloro-substituents, are eliminated extremely
slowly: for example, the half-life of 2,3,7,8tetrachlorodibenzodioxin (TCDD) is about 8
years in humans.
Classical Toxicokinetics
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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 Model
The 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 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 model
Two-Compartment Model
After rapid iv administration of some toxicants, the semilogarithmic 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 elimination
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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 halflife 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
where
Cp = Concentration in plasma
Vss= Volume of Distribution at steady state
F = Fractional bioavailability of the dose
Dosing Rate
In the majority of clinical situations, drugs are
administered as a series of repeated doses or as
a 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
where
CL= Clearance
F= Fractional bioavailability of the dose