TOXICOKINETICS

Xenobiotis with there biotransformation

1. TOXICOKINETICS

RVS Chaitanya Koppala
Assistant professor
Vignan Institute of Pharmaceutical Technology
Visakhapatnam

2. TOXICOKINETICS
The term toxicokinetic was first used by a Russian author in 1937. Since then, it has gained
popularity. Yacobi et al (1989) defines toxicokinetic as “the application of pharmacokinetics
principles to the investigation of toxicity and other adverse effects of drugs” according to ICH,
Toxicokinetic “the generation of pharmacokinetic data either as an integral component of non-
clinical toxicity studies or specially designed supportive studies to assess systemic exposure”.
Toxicokinetic studies differ from pharmacokinetic studies primarily with respect to dose. The
former is generally carried out at much higher doses than those used in pharmacokinetic studies.
Data derived from toxicokinetic studies helps to assess the safety profile of a chemical agent at
toxic dose levels while pharmacokinetic data is employed for chemical agent characterization.
Objectives:
1. To measure the systemic exposure of a chemical agent attained at various dose levels
2. To correlate the systemic exposure obtained with toxicological findings and thus help
in the assessment of the relevance of these finding to clinical safety of a drug.
Toxicokinetic concepts
Toxicokinetic can be described as the study of modelling and mathematical description of the
time course of desposition of chemical in the animals and humans. Two models are available
to estimate the time course of desposition of xenobiotics, the classical model and the
physiological model.
1. Classical model:
It comprises of plasma and highly perfused tissues like kidneys, brain, lung, liver and
heart. It rapidly equilibrates with the chemical.
2. Peripheral component
It comprises of tissues with low and poor vascularity like adipose tissue, skin, bones,
teeth etc. these tissues slowly equilibrate with the chemical.
a) one compartment open model:
simples’ model of all the compartment models. The term open represent that the administered
chemical agent can be eliminated from the body and also the output (absorption) and output
(elimination) of the administered chemical agent are unidirectional. One compartment open

3. model helps in determining the plasma levels of a chemical agent after the administration of a
single dose.

Any chemical agent administered intravenously bypasses its absorption phase i.e. the
absorption is so rapid and instantaneous that it can be neglected. This enable in rapid
distribution (within 1-3 minutes) of the chemical agent throughout the body via systemic
circulation.

The general expression for the chemical agent administered as i.v bolus is represented as
dX/dt = chemical agent input (absorbed drug)-chemical agent output (chemical agent
to be eliminated)
Where
dX/dt = rate of change of chemical agent concentration with respect to time.
Since the absorption process is neglected for drugs given as i.v bolus, therefore the above
relation becomes.
dX/dt = chemical agent output (chemical agent to be eliminated)
Since we know that, the administration of a chemical agent through i.v route follow first order
kinetics
dX/dt = -KEX -------- 1
Where, KE= First order elimination rate constant

4. X= amount of chemical agent to be eliminated
Note: negative sign in the equation indicates chemical agent loss from the body
Elimination Rate constant (K
E
)
Elimination rate constant (KE) can be obtained by integrating equation (1)
dX/dt = KEX
lnX=ln X0-KEt ------------- 2
Taking log on both sides we get
Log X = log X0-KEt/2.303 ------------ 3
Since the amount of chemical agent in the body X is equal to the product of the chemical
agent concentration in plasma C and its volume of distribution Vd
X = Vd C
Since Vd is the proportionally constant it allows the use of C in place of X
Equation (3) can be written as
log C=log C0-KE
t
/2.303 ----------------4
Where
C0= concentration of chemical agent in plasma attained just after its i.v administration
i.e at t = 0
Equation 4 is in the form of a straight-line
y = mx + c

Therefore, a plot of log C vs
t
gives a straight line with slope -KE/ 2.303 and
y
-intercept
log C0

5. Elimination /biological half-life (t ½):
Elimination or biological half-life of a chemical agent is defined as the time taken for
the reduction of the total amount of chemical agent in the body including plasma
chemical agent concentration to half of its original value. The units of t1/2 are hours or
minutes. It is given by
t ½= 0.693/KE
Apparent volume of distribution:
Since the amount of chemical agent in the body X is equal to the product of plasma
chemical agent concentration C and its volume of distribution Vd
X = Vd C
Vd = X / C
Vd is known as apparent volume of distribution it is only a hypothetical value and does
not have any actual physiological meaning in terms of an anatomical space.
Apparent Vd represents the extent of chemical agents’ distribution in the body and is
expressed in liters.
Determination of Vd
Vd of chemical agent can be determined by administering it rapidly via i.v route. In a
one compartment mode. Vd is given by
Vd = X0/C0
Where
X0= i.v bolus dose
C0 = Initial plasma chemical agent concentration at t=0
However, the above formula can only be used only for drug that follow one
compartment kinetics after the attainment of chemical agent distribution equilibrium
between the blood and tissues

6. Significance of Vd:
1. Vd helps to correlate the amount of chemical agents in the body with the concentration of
chemical agent in systemic circulation (plasma)
2. Large Vd implies that the chemical agent is more concentrated in extravascular tissues and
less concentrated intravascularly
3. Vd of a chemical agent indicates its general ability to dissolve in fat. Bind with extravascular
macromolecules or to penetrate the biological membranes
4. It is also useful in therapeutic drug monitoring in certain diseased condition
5. It serves as an important parameter in determining the appropriate drug dosing regimens
6. Since Vd is directly related to total clearance, therefore, an increase or decrease in Vd will
correspondingly increase or decrease the ClT
Clearance:
The capacity of the organ or the whole organism to remove the chemical agent by metabolism
and or excretion is known as clearance. It may be defined as the hypothetical volume of body
fluids from which the chemical agents have been completely removed in a specified period of
time.
Units: ml/min/ or litre/hr.
It is the ratio of rate of elimination of chemical agent dx/dt and drug concentration in plasma C
Cl = rate of elimination n of drug (dX/dt) /drug concentration in plasma C
Or
Cl = dX / dt / C
The concept of drug clearance is used to study the complex mechanisms of drug elimination by
quantifying the rate and extend to drug elimination from the whole body or from the different
organ of the body. The organs involved in drug clearance include lungs, kidneys, liver, skin,
intestine etc. the clearance of drugs from these organs can be calculated by determining their
ratio of elimination rate by the specific organ of the drug concentration in plasma.
Hepatic clearance (ClH) = Rate of elimination n through liver / C
Renal clearance (ClR) = Rate of elimination through kidney / C
Clearance form other organs Clothers = Rate of elimination from other organs/ C

7. Total systemic clearance (ClT) or total body clearance can therefore be expressed as the sum of
renal clearance ClR, hepatic clearance ClH and clearance from other organs Clothers
Therefore ClT = ClH + ClR+ Clothers
However, clearance from organs other than kidneys is generally termed as non-renal clearance
(Clnr)
Consider equation (1), ClT = dX/dt /C
But we know that
dX/dt = KEX
Substituting this value in the above equation we get
ClT = [X / C] Ke --------------- 2
From the definition of Vd, we have seen that Vd = X/C
Substituting this value in equation (2) we get
ClT = Vd Ke ---------------- 3
From the definition of elimination half-life, we have seen that t1/2 = 0.693/Ke
Substituting this value in equation 3
ClT = Vd 0.693 / t1/2 ------------------ 4
Similarly, for ClR and ClH the above reaction may be written as
ClR = Vd 0.693/t1/2 (where t1/2 is excretion half life for unchanged drug)
ClH = Vd 0.693/t1/2 (where t ½ is metabolism half life)
b) multicompartment models:
 In one compartment models, the drug following i.v administration distributes itself
instanteously and rapidly into the highly vascularized central compartment.
 The plasma level time curve of drugs following one compartment model reflects first
order kinetics and the drug disposition is expressed by an equation with a
monexponential term.

8.  However, a large number of drugs do not attain instantaneous distribution in all the
tissues because of difference in factors such as rates of perfusion of the tissues and
affinity of the chemical agents for a particular tissue. Such drugs will take a long time
to establish distribution equilibrium between the central and the peripheral (tissue)
compartment resulting in non linear plasma level time profile.
 Multicompartment models were developed to explain the behavior and to predict the
plasma and tissue concentrations of drugs which possess selective affinity towards a
particular tissue.
 Like one compartment model, the kinetic analysis of multi compartment model also
assume that drug disposition occurs by first order kinetics. The multicompartment
properties of a drug as best understood by administering i.v bolus and observing its
plasma concentration time profile. The more the number of peripheral compartments
that equilibrate with the central compartment, the more will be the exponential terms (bi
or multi) describing the plasma level time curve. Once the chemical agents attains
equilibrium between the central and peripheral compartment, the elimination takes place
monoexponentially i.e follow first order kinetics.
 The different multicompartment models used are two compartment and three
compartment models. In two compartment open model. The drug distribution occurs
between central compartment comprising of highly vascularized tissues like brain, liver,
kidney, lungs and the peripheral compartment consisting of less vascularized tissues like
skins, muscles etc.




Three compartment models consisting of a central compartment (1), peripheral compartment
(2) and a very poorly vascularized third compartment called peripheral compartment (3) which
comprises of poorly perfused tissue like bone, hair and adipose tissue.

9. Two compartment open model
It’s the most common of all the multicompartment models. The plasma level time curve for a
chemical agent following two compartment model shows a biexponential decline in the
chemical agent concentration which is the sum of two first order kinetics processes i.e
distribution and elimination.
The decline in the chemical agent concentration from the central compartment is due to:
1. Distribution of chemical agent from central compartment to peripheral compartment
(distribution phase)
2. Elimination of chemical agent from central compartment (elimination phase)
There are three possible two compartment models depending upon the compartment from.
Which the chemical agent is eliminated.

10. K12 and K21 are the rate constant for the transfer of drugs between central and peripheral
compartment. These are also referred to as micro constants.
The important points to be considered while developing equations for a two-compartment open
model are:
1. Chemical agent distribution occurs between central and peripheral compartment. Chemical
agents distribute rapidly in central and slowly in peripheral compartment.
2. Transfer of chemical agent between two compartment takes place by first order process
3. Chemical agent elimination is always presumed to occur from central compartment since
the major organs of chemical agents’ elimination i.e. kidney and liver are located centrally.
4. Chemical agent elimination is assumed to occur by first order kinetics.
5. The chemical agent concentration in a compartment is assumed to be uniform in its volume
of distribution, the chemical agent concentration in the peripheral compartment will first
increase, reach maximum and then decline.
6. It is assumed that at time zero the peripheral compartment is devoid of any drug. Following
i.e. i. v administration. The chemical agent concentration in the peripheral compartment will
first increase, reach maximum and then decline.

11. Following i.v bolus injection, the plasma level time curve shows an initial rapid decline in
concentration from the central compartment. This is called distributive phase. During this phase,
the chemical agent rapidly diffuses from the central compartment into the tissue / peripheral
compartment
Following this, the fraction of chemical agent in tissue compartment first increases and then
reaches to maximum which indicates equilibrium between the two compartments. After
attaining maximum tissue concentration. The rate of chemical agent entry into the tissue equals
the rate of parallel chemical agents exit from the central compartment. Since, chemical agent
elimination and distribution occur concurrently in central compartment, there occur a slow
decline in the chemical agent concentration from the both the compartments. This corresponds
to the elimination phase.

According to mass balance equation, the rate of changes in chemical agent concentration in
central and peripheral compartments is the net changes of rate of input and rate of output.
Therefore, the rate of changes in drug concentration in central compartment is given as
dC/dt = K
21
C
P
– K
12
C
E
-K
E
C
E

= K
21
X
P
/V
P
– K
12
X
C
/V
C
-K
E
X
C
/V
C
(Since X
c
= V
c
C
c
)
Similarly, the rate of change in drug concentration in peripheral compartment is given by
dC
p
/dt = K
12
C
C
-K
21
C
P

= K
12
X
c
/ V
c
-K
21
X
P
/ V
P

12. Integration of equation (1) and (2) gives concentration of drug in central and peripheral
compartment at any given time t

13. SATURATION (NON-LINEAR) TOXICOKINETICS:
As the dose of the chemical increase the elimination rate, volume of distribution etc. changes
and the toxicokinetic profile shows a mixture of both first order kinetics and zero order kinetics.
This behavior is termed as saturation toxicokinetic and is of importance it results in increased
concentration at the target site of action which leads to enhanced toxicity
The most common reason for non-linearity is that many of the process of drug ADME involves
carriers and enzymes which are substrate specific and have definite capacities. At increased
doses, these enzymes or carrier mediated systems gets saturated resulting in the transformed of
first order kinetics into mixed order.
Nonlinear toxicokinetic is indicated by:
1. Non linearity in elimination
2. Changes in elimination half-life with dose, at higher doses, t1/2 increases due to
saturation of enzymes systems with low dose, t1/2 might decrease due to enzyme
induction.
3. AUC is not proportional to the amount of bioavailable drug.
4. Composition and / or ratio of drug metabolites get affected by changes in the dose
5. Drugs dependent on the same enzymes or carrier mediated system may affect the
saturation of capacity limited process.
2. Physiological models: In these models, the rate constants represent hypothesized or known
biological processes. They often resemble like two or more classic one compartment models
connected together by the circulatory system. The basic unit of physiological model is the
lumped compartment, which consists of the vascular space which perfuses compartment with
blood the interstitial space surrounding the cell and the intercellular space composed of the cells
in the tissue.

14. Q = blood flow rate
HPT = Highly perfused tissues
PPT = poorly perfused tissue
Ke = first order rate constant for urinary excretion
Km = rate constant for hepatic elimination
a)
Perfusion rate limited models:
these models are based on the assumption that the
movement of toxicant within a region of the body is dependent on the rate of perfusion.
Movement into and out of the tissue is given by.

Where
V1 = volume of tissue compartment
C1 = concentration of free chemical in the compartment
V1 dC1/ dt = the change in the amount of chemical in the compartment with time

15. Q1 = the blood flow to tissue
C
in = concentration of chemical entering in the compartment
C
out = concentration of chemical leaving the compartment
In perfusion limited case Cout
= C
1
/ P
1
Where P1 = partition coefficient of tissue
Therefore, the above equation changes to




b)
Diffusion limited models:

These models are based on the assumptions that uptake of atoxicant into a compartment is
governed by its diffusion across cell membrane barriers. Diffusion limited uptake occurs
when the movement of toxicant across the cell membrane is relatively slow to the flow of
blood to the tissue. Movement of toxicant into and out of the tissue is given by

c) Specialized compartments:
1. Lung: is included in a physiological model because many toxicants enter via. Inhalation
route, following assumptions are made with regard to lung compartments
 Ventilation is a continuous process but not cyclic
 Conducting airways are inert tubes that transport the vapour to the alveoli
 The rate at which vapor diffuses across the alveolar epithelium and capillary walls
is faster than the rate of blood flow through alveolar region.
 Hold up of chemicals in the lungs in insignificant.

16.  Vapour present in the alveolar air and arterial blood exist in equilibrium
 These assumptions simplify model calculation and is sufficient for describing the
toxicokinetic of relatively inert vapour
 with poor aqueous solubility
The rate of change in the amount of toxicant in the lung compartment is described by:
dl/dt= Q
P
(CI
NH
– C
ALV
) + Q
E
(C
VEN
- C
ART
)
Where:
Q
p = Ventilation rate
C
inh = Inhaled concentration of toxicant
C
alv = Toxicant concentration in the alveoli
Q
C = Cardiac output
C
ven = Concentration in venous blood
C
art = Concentration in arterial blood
ii) Liver: is included in physiological models because many toxicants are bio transformed in
liver. Liver compartment is similar to a tissue compartment and in addition it contains process
for metabolic elimination. If the rate of elimination follows first order kinetics, then the rate of
hepatic metabolism given by:

iii) Blood: a separate blood component is included in the physiological model if the
toxicokinetic after i.v dose is stimulated or if binding of toxicant to blood components or
metabolism of toxicant by blood compartment suspected.