1. The document discusses intravenous (IV) infusion of drugs using a one-compartment open model. It describes the assumptions of this model and how drug concentrations in plasma can be calculated based on the rate of IV infusion, volume of distribution, and drug elimination rate constant. 2. A key point is that IV infusion allows precise control of drug concentrations in plasma to fit individual patient needs and maintain therapeutic levels. It also minimizes fluctuations in drug levels. 3. The model shows that drug levels will increase during IV infusion until reaching a steady-state concentration where the rates of drug input and elimination are equal. The time to reach 95% of steady-state can be calculated from the drug half-life.

1. Intravenous Infusion after One
Compartment open model
Applied Biopharmaceutics & Pharmacokinetics (Sixth edition)
Page 91-98
Applied Biopharmaceutics & Pharmacokinetics (Seventh edition)
Ch#6, Page 131-140

2. Introduction
• Drugs may be administered to patients by oral, topical, parenteral, or
other various routes of administration.
• Examples of parenteral routes of administration include intravenous,
subcutaneous, and intramuscular.
• Intravenous (IV) drug solutions may be either injected as a bolus dose
(all at once) or infused slowly through a vein into the plasma at a
constant rate (zero order).

3. Advantages of IV infusions
The main advantage for giving a drug by IV infusion is:
1. It allows precise control of plasma drug concentrations to fit the
individual patient needs.
2. For drugs with a narrow therapeutic window (eg, heparin), IV infusion
maintains an effective constant plasma drug concentration
3. It eliminates wide fluctuations between the peak (maximum) and trough
(minimum) plasma drug concentration.
4. IV infusion of drugs eg, antibiotics, may be given with IV fluids that
include electrolytes and nutrients.
5. The duration of drug therapy may be maintained or terminated as
needed using IV infusion.

4. Illustration
IV infusion can give high degree of precision by infusing drugs via a drip or
pump in hospitals
4

5. Assumptions in One-compartment open
model after IV infusion
• Whole body is composed of a single compartment where the drug is
to be distributed.
• The pharmacokinetics of a drug given by constant IV infusion follows
a zero-order input process in which the drug is directly infused into
the systemic blood circulation.
• Elimination of drug from the plasma is a first-order process.

6. Graph for IV infusion.
• The plasma drug concentration-time curve of a drug given by
constant IV infusion is shown.
• Because no drug was present in the body at zero time, drug level rises
from zero drug concentration and gradually becomes constant when a
plateau or steady-state drug concentration is reached.
• At steady state, the rate of drug leaving the body is equal to the rate
of drug (infusion rate) entering the body. Therefore, at steady state,
the rate of change in the plasma drug concentration dCp/dt = 0, and
• Rate of drug input (infusion rate) = rate of drug output (elimination
rate)

7. Graph for IV infusion.
• Plasma level-time curve for constant IV infusion.

8. One-compartment Model Drugs
• In one-compartment model, the infused drug follows zero-order input
and first-order output.
• The change in the amount of drug in the body at any time (dDb/dt)
during the infusion is the rate of input minus the rate of output.
• dDB = R - kDB
dt
• DB = the amount of drug in the body
• R = infusion rate (zero order)
• k = elimination rate constant (first order).

9. One-compartment Model Drugs
• Integration of the above equation and substitution of DB = CpVD gives:
• The above equation gives plasma drug concentration at any time
during the IV infusion, where t is the time for infusion.
• As the drug is infused, the value for certain time (t) increases in
Equation.
)
1
( t
k
el
d
p
el
e
k
V
R
C 



10. One-compartment Model Drugs
• At infinite time t = ∞, e^-kt approaches zero, and Equation reduces to
Equation as the steady-state drug concentration (Css).
)
1
( 


 e
k
V
R
C
el
d
p
Cl
R
k
V
R
C
el
d
ss 


11. Steady-State Drug Concentration (Css) and
Time Needed to Reach Css
• The Css equation may also be
obtained with the following
approach.
• At Css, the rate of infusion equals
the rate of elimination. Therefore,
the rate of change in the plasma
drug concentration is equal to
zero.
• Equation shows that Css is
dependent on the volume of
distribution, the elimination rate
constant, and the infusion rate.

13. Steady-State Drug Concentration (Css) and
Time Needed to Reach Css
• Once the steady state is reached, the rate of drug leaving the body is equal to the
rate of drug entering the body (infusion rate).
• In other words, there is no net change in the amount of drug in the body, DB, as a
function of time during steady state.
• Drug elimination occurs according to first-order elimination kinetics.
• Whenever the infusion stops, either before or after steady state is reached, the
drug concentration always declines according to first-order kinetics.
• The slope of the elimination curve equals to -k/2.3.
• Even if the infusion is stopped before steady state is reached, the slope of the
elimination curve remains the same.
• In clinical practice, a plasma drug concentration prior to, the theoretical steady
state is considered the steady-state plasma drug concentration (Css).

14. Steady-State Drug Concentration (Css) and
Time Needed to Reach Css
• Plasma drug concentration-
time profiles after IV infusion
is stopped at steady state (A)
or prior to steady state (B) is
shown.
• In both cases, plasma drug
concentrations decline
exponentially (first order)
according to a similar slope.

15. Steady-State Drug Concentration (Css) and
Time Needed to Reach Css
• Mathematically, the time to reach true steady-state drug concentrations, Css,
would take an infinite time.
• The time required to reach the steady-state drug concentration in the plasma is
dependent on the elimination rate constant of the drug for a constant volume of
distribution.(K and Vd)
• In clinical practice, the drug activity will be observed when the drug
concentration is close to the desired plasma drug concentration, which is usually
the target or desired steady-state drug concentration.
• The time to reach 90%, 95%, and 99% of the steady-state drug concentration, Css,
may be calculated.
• For therapeutic purposes, the time for the plasma drug concentration to reach
more than 95% of the steady-state drug concentration in the plasma is often
estimated.

16. Steady-State Drug Concentration (Css) and
Time Needed to Reach Css
• How much time is required for a drug to reach at least 95 % of steady
state plasma drug concentration. Half life of the drug is 6 hours.

18. Steady-State Drug Concentration (Css) and
Time Needed to Reach Css
• An increase in the infusion rate will not shorten the time to reach the
steady-state drug concentration
• If the drug is given at a more rapid infusion rate, a higher steady-
state drug level will be obtained, but the time to reach steady state is
the same.

19. Infusion Method For Calculating Patient
Elimination Half-life (t ½ el).
• The Cp-versus-time relationship that occurs during an IV infusion may
be used to calculate k, or indirectly the elimination half-life of the
drug in a patient.
• Some information about the elimination half-life of the drug in the
population must be known, and one or two plasma samples must be
taken at a known time after infusion.
• Knowing the half-life in the general population helps determine if the
sample is taken at steady state in the patient.
• To simplify calculation, IV infusion Equation is arranged to solve for k:

20. Infusion Method For Calculating Patient
Elimination Half-life

21. Infusion Method For Calculating Patient
Elimination Half-life
• where Cp = plasma drug concentration taken at time t
• Css = approximate steady-state plasma drug concentration.
t ½ = 0.693
K

22. LOADING DOSE PLUS IV INFUSION—
ONE-COMPARTMENT MODEL
• The loading dose DL, or initial bolus dose of a drug, is used to obtain
desired concentrations as rapidly as possible.
• The concentration of drug in the body for a one-compartment model
after an IV bolus dose is described by:
• And conc by infusion at the rate R is given as:
t
k
d
L
t
k
p
el
el
e
V
D
e
C
C 



 
1
)
1
(
2
t
k
el
d
el
e
k
V
R
C 



23. LOADING DOSE PLUS IV INFUSION—
ONE-COMPARTMENT MODEL
• Assume that an IV bolus dose DL of the drug is given and that an IV
infusion is started at the same time.
• The total concentration Cp at t hours after the start of infusion would
be equal to C1 + C2 due to the sum contributions of bolus and
infusion:

24. LOADING DOSE PLUS IV INFUSION—
ONE-COMPARTMENT MODEL
• The loading dose needed to get immediate steady-state drug
levels can also be found by the following approach.
• Loading dose equation:
• Infusion eqn:
• Adding up the two equations yields an equation describing
simultaneous infusion after a loading dose.
)
1
( t
k
el
d
t
k
d
L
p
el
el
e
k
V
R
e
V
D
C 




)
1
(
2
t
k
el
d
el
e
k
V
R
C 


1
)
1
( t
k
el
d
t
k
d
L
p
el
el
e
k
V
R
e
V
D
C 





25. LOADING DOSE PLUS IV INFUSION—
ONE-COMPARTMENT MODEL
• Let the loading dose (DL) equal the amount of drug in the body at steady state
• DL = Css.VD
• From the Css we can say that, Css.VD = R/k. Therefore:
• DL = R/k
• Substituting DL = R/k in Cp equation, makes the expression in parentheses cancel
out. The equation thus obtained is same as that of the Css equation.ie,
• Therefore, if an IV loading dose of R/k is given, followed by an IV infusion, steady-
state plasma drug concentrations are obtained immediately and maintained.
el
d
p
k
V
R
C 
el
d
ss
k
V
R
C 

26. LOADING DOSE PLUS IV INFUSION—
ONE-COMPARTMENT MODEL
• Another method for the calculation of loading dose (DL) is based on
knowledge of the desired Css and the apparent volume of distribution
VD for the drug, as shown in Equation.
DL = Css.VD
• For many drugs, the desired Css is reported in literature as the
effective therapeutic drug concentration.
• VD and the elimination half-life are also available for these drugs.

27. Answer me !!!

29. Question

31. LOADING DOSE PLUS IV INFUSION—
ONE-COMPARTMENT MODEL
• The graph is of combined IV infusion
with loading dose DL. The loading
dose is given by IV bolus injection at
the start of the infusion.
• Plasma drug concentrations decline
exponentially after DL whereas they
increase exponentially during the
infusion.
• The resulting plasma drug
concentration-time curve is a straight
line due to the summation of the two
curves.

32. LOADING DOSE PLUS IV INFUSION—
ONE-COMPARTMENT MODEL
• In order to maintain instant steady-state level ([dCp/dt] = 0), the loading dose
should be equal to R/k.
• If the DL and infusion rate are calculated such that C0 and Css are same and both
are started concurrently, then Css will be achieved immediately after the loading
dose is administered.
• In the figure below, curve b shows the blood level after a single loading dose of
R/k plus infusion from which the concentration desired at steady state is
obtained.
• If the DL is not equal to R/k, then steady state will not occur immediately.
• If the loading dose given is larger than R/k, the plasma drug concentration takes
longer to decline to the concentration desired at steady state (curve a).
• If the loading dose is lower than R/k, the plasma drug concentrations will increase
slowly to desired drug levels (curve c), but more quickly than without any loading
dose (curve d).

33. LOADING DOSE PLUS IV INFUSION—
ONE-COMPARTMENT MODEL

34. ESTIMATION OF DRUG CLEARANCE AND Vd
FROM INFUSION DATA
• Previously, the plasma concentration of a drug during constant infusion
was described in terms of Vd and elimination constant k.
• Alternatively, the equation may be described in terms of clearance by
substituting for k = Cl/VD:
• When a constant volume of distribution is evident, the time for steady
state is then inversely related to clearance. Thus, drugs with small
clearance will take a long time to reach steady state
)
1
( t
k
el
d
p
el
e
k
V
R
C 



35. INTRAVENOUS INFUSION OF TWO-
COMPARTMENT MODEL DRUGS
Shargel 7th edition, page # 141-144

36. Illustration

37. Introduction
• Many drugs given by IV infusion follow two-compartment kinetics.
Example, theophylline and lidocaine.
• With two-compartment-model drugs, IV infusion requires a distribution
and equilibration of the drug before a stable blood level is reached.
• During a constant IV infusion, drug in the tissue compartment is in
distribution equilibrium with the plasma; thus, constant Css levels also
result in constant drug concentrations in the tissue, that is, no net change
in the amount of drug in the tissue occurs during steady state.
• Although some clinicians assume that tissue and plasma concentrations are
equal when fully equilibrated, kinetic models only predict that the rates of
drug transfer into and out of the compartments are equal at steady state.
In other words, drug concentrations in the tissue are also constant, but
may differ from plasma concentrations.

38. Introduction
• The time needed to reach a steady-state blood level depends
entirely on the distribution half-life of the drug.
• The equation describing plasma drug concentration as a function of
time is as follows:
• where a and b = hybrid rate constants
• R = rate of infusion.
• At steady state (ie, t = ∞), the above equation reduces to:

39. Infusion rate
• By rearranging this equation, the infusion rate for a desired steady-
state plasma drug concentration may be calculated.

40. Loading Dose for Two-Compartment Model Drugs
• Drugs with long half-lives require a loading dose to more rapidly
attain steady-state plasma drug levels.
• It is clinically desirable to achieve rapid therapeutic drug levels by
using a loading dose.
• However, for a drug that follows the two- compartment
pharmacokinetic model, the drug distributes slowly into extravascular
tissues. Thus, drug equilibrium is not immediate.
• The plasma drug concentration of a drug that follows a two-
compartment model after various loading doses is shown.

42. Loading Dose for Two-Compartment Model
Drugs
• If a loading dose is given too rapidly, the drug may initially give
excessively high concentrations in the plasma (central compartment),
which then decreases as drug equilibrium is reached.
• It is not possible to maintain an instantaneous, stable steady-state
blood level for a two-compartment model drug with a zero-order rate
of infusion.
• Therefore, a loading dose produces an initial blood level either slightly
higher or lower than the steady-state blood level. To overcome this
problem, several IV bolus injections given as short intermittent IV
infusions may be used as a method for administering loading dose to
the patient.

44. Apparent Volume of Distribution at Steady
State, Two-Compartment Model
• The apparent volume of drug at steady state (Vd)ss may be calculated
by dividing the total amount of drug in the body by the concentration
of drug in the central compartment at steady state:
• Can also be expressed as:

46. Apparent Volume of Distribution at Steady
State, Two-Compartment Model
• (VD)ss is a function of transfer rate constants k12 and k21.
• The magnitude of (VD)ss is dependent on the hemodynamic factors
responsible for drug distribution and on the physical properties of the
drug, which, in turn, determine the relative amount of intra- and
extravascular drug.
• Unlike (VD)β, (VD)ss is not affected by changes in drug elimination.
• (VD)ss reflects the true distributional volume occupied by the
plasma and the tissue pool when steady state is reached.
• (VD)ss is several times greater than Vp( volume of the plasma
compartment).

47. Apparent Volume of Distribution at Steady
State, Two-Compartment Model
• Another volume term used in two-compartment modeling is (VD)β.
(VD)β = Cl /β
• (VD)β depends on drug elimination by phase