Pharmacodynamic models along with relationship between dose, pharmacological effect, duration of activity and elimination half life.

1. PHARMACOKINETIC AND
PHARMACODYNAMIC
CORRELATION
Dr. Ramesh Bhandari
Asst. Professor
Department of Pharmacy Practice,
KLE College of Pharmacy, Belagavi

2. Pharmacodynamics is the study that establishes
and elucidates relationships between
concentrations of a drug at the receptor or target
organ (effect site) and the intensity of its
pharmacological effect.
Pharmacodynamics deals with the relationship
between drug concentrations at the effect site or
concentrations (usually unbound concentrations) in
plasma in equilibrium with effect site
concentrations, and the magnitude of the observed
pharmacological effect of the drug.

3. The effect site (site of action) of a drug can be a
target receptor/enzyme(s) or an organ(s) where the
initial pharmacological responses to the drug are
produced.
The pharmacological activity of a drug generally
includes a series of sequential events, i.e.,
interaction of drug molecules with their action sites
or receptors, induction of a stimulus to the effector
systems, and subsequent production of the effect
(observed pharmacological endpoints).

4. Characteristics of Pharmacological Responses
All-or-None vs. Graded Responses
Direct vs. Indirect Responses
Reversible vs. Irreversible Responses

5. Differences among Pharmacokinetics, the
Pharmacokinetic/Pharmacodynamic Relationship, and
Pharmacodynamics
Dose Cp(t) Ce(t) Effect
Stage 1 Stage 2 Stage 3
PK PK/PD PD

6. 1. STAGE 1: The relationship between the dose and the time
course of drug concentrations in biological fluids
(pharmacokinetics).
2. STAGE 2: The time-dependent relationship between the
drug concentrations in biological fluids such as plasma and
at the effect site, which can be established by linking
pharmacokinetics and pharmacodynamics of the drug with
PK/PD modeling approaches (pharmacokinetic and
pharmacodynamic relationship).
3. STAGE 3: The relationship between drug concentration at
effect site and the observed pharmacological effects
(pharmacodynamics).

7. PHARMACODYNAMIC MODELS
Pharmacodynamic models are mathematical schemes
based on classical receptor theory for an empirical
description of the intensity of a pharmacological
response to a drug as a function of its concentrations at
the effect site.
Pharmacodynamic models are useful for describing the
apparent pharmacodynamic profiles of a drug.

8. Types of Pharmacodynamic Models
1)Linear Model
2)Log-Linear Model
3)Emax Model
4)Sigmoid Emax Model
5)Inhibitory Emax Model

9. Linear Model
The linear pharmacodynamic model is useful when
the efficacy of a drug is proportional to its
concentrations at the effect site. The linear model
can be derived from the Emax model, when its
concentrations at the effect site is significantly
lower than EC50.
E = S. Ce + E0

10. Fig: Linear Model
Effect
(E)
Drug Concentration at the effect site (Ce)
E
0

11. Log-Linear Model
The log-linear model is based on the empirical
observation that a plot of effect vs. log
concentration of many drugs exhibits a linear
approximation between 20 and 80% of the
maximum effect. Like the linear model, the
concentration-effect relationship within this range
can be analyzed using linear regression.
E = S log Ce + I

12. Effect
(E)
Drug Concentration at the effect site (log Ce)
I
Fig: Log-linear Model

13. Emax Model
The Emax model can describe the concentration--effect
curve over the full range from the baseline effect to the
maximum effect of a drug. Accurate measurement of both
Emax and EC50 are critical in the Emax model. In fact,
only a few drugs have been shown to have this
relationship in vivo mainly owing to the difficulties
involved in conducting studies over a wide range of
concentrations, especially at high concentrations because
of the concomitant potential toxicity.
𝐸 = 𝐸𝑚𝑎𝑥.
𝐶𝑒
𝐸𝐶=𝐶𝑒
+ E0

14. Emax
Effect
(E)
EC50
Drug Concentration at the effect site (Ce)
Fig: Emax Model

15. Sigmoid Emax Model
The sigmoid Emax model can be used when the
concentration-effect curve exhibits more an S-shape
pattern than a simple hyperbola (the Emax model),
and is steeper or shallower than predicted by the
Emax model. The sigmoid function originally
proposed by Hill (1910) is often called the Hill
equation.
𝐸 = 𝐸𝑚𝑎𝑥.
𝐶 𝑛
𝑒
𝐸𝐶 𝑛
50
+𝐶𝑛𝑒
+ E0

16. Emax
Effect
(E)
EC50
Drug Concentration at the effect site (Ce)
Fig: Emax Model
n=1
n<1
n>1

17. MODEL CHARACTERISTICS
Linear  Predicts the baseline effect when the concentration is
zero
 Unable to define the maximum effect at high
concentration
 Error- prone at high or low drug concentration
Log-Linear  Suitable for predicting drug effects over 20-80 % of the
maximum effect
 Unable to define the baseline and the maximum effects
Emax  Able to describe the pharmcodynamic relationship over a
wide range of drug concentrations
 Predict the baseline and the maximum effects.
Sigmoid Emax  Able to describe S-shape pattern of effect curve by
adjusting n values
 Predict the baseline and the maximum effects

18. RELATIONSHIP OF DOSE TO
PHARMACOLOGICAL EFFECT
 The onset, intensity, and duration of the pharmacologic effect
depend on the dose and the pharmacokinetic of the drug.
 As the dose increases the drug concentration at the receptor site
increases, and the pharmacologic response increases up to maximum
effect.
 A plot of the pharmacologic effect to dose on a linear scale generally
results in hyperbolic curve with maximum effect at the plateau.

19. RELATIONSHIP OF DOSE TO
PHARMACOLOGICAL EFFECT
 A plot of the
pharmacologic
effect to dose on a
linear scale
generally results in
hyperbolic curve
with maximum
effect at the plateau.

20. RELATIONSHIP OF DOSE TO
PHARMACOLOGICAL EFFECT
 Same data may be
compressed and plotted
on a log linear scale and
result in a sigmoid
curve.

21. RELATIONSHIP OF DOSE TO
PHARMACOLOGICAL EFFECT
For many drugs, the graph
of the log dose response
curve shows a linear
relationship at a dose
range between 20-80% of
the maximum response,
which typically includes
the therapeutic dose range
for many drugs.

22. RELATIONSHIP BETWEEN DOSE AND DURATION
OF ACTIVITY (teff), SINGLE IV BOLUS INJECTION
 Relationship between the duration of the pharmacologic effect and the
dose can be given by following equation:
Log C = log C0 – (k/2.3)
 After an intravenous dose, assuming a one-compartment model, the time
needed for any drug to decline to a concentration C is given by the
following equation, assuming the drug takes effect immediately:
t = 2.3 (log C0 – log C)/k

23. RELATIONSHIP BETWEEN DOSE AND DURATION
OF ACTIVITY (teff), SINGLE IV BOLUS INJECTION
Using Ceff to represent the minimum effective drug
concentration, the duration of drug action can be obtained as
follows:
teff = 2.3 [log(D0/VD) – log Ceff] / k
For example, a doubling of the dose will not result in a
doubling of the effective duration of pharmacologic action.
A doubling of t1/2 or a corresponding decrease in k will result in
a proportional increase in duration of action.

24. EFFECT OF BOTH DOSE AND ELIMINATION
HALF LIFE ON THE DURATION OF ACTIVITY
 An increase in t1/2 will increase the teff in direct
proportion.
 An increase in the dose, D0, does not increase the teff
in direct proportion.
 A nonlinear increase in teff is observed as dose
increases.

25. EFFECT OF ELIMINATION HALF LIFE ON
DURATION OF ACTIVITY
Elimination of drugs is due to the processes of excretion and
metabolism, an alteration of any of these elimination
processes will affect the t1/2 of the drug.
In certain disease states, pathophysiologic changes in hepatic
or renal function will decrease the elimination of a drug, as
observed by a prolonged t1/2.
This prolonged t1/2 will lead to retention of the drug in the
body, thereby increasing the duration of activity of the drug
(teff) as well as increasing the possibility of drug toxicity

26. EFFECT OF ELIMINATION HALF LIFE ON
DURATION OF ACTIVITY
To improve antibiotic therapy with the penicillin and
cephalosporin antibiotics, clinicians have intentionally
prolonged the elimination of these drugs by giving a second
drug, probenecid, which competitively inhibits renal
excretion of the antibiotic.
This approach to prolonging the duration of activity of
antibiotics that are rapidly excreted through the kidney has
been used successfully for a number of years

27. EFFECT OF ELIMINATION HALF LIFE ON
DURATION OF ACTIVITY
Dose (mg/kg) t1/2 = 0.75h
teff (h)
t1/2 = 1.5 h
teff (h)
2.0 3.24 6.48
3.0 3.67 7.35
4.0 3.98 7.97
Above example shows how a change in the elimination t1/2
will affect the teff for a drug.
For all doses, doubling the t1/2 will double the teff.
However, the effect of doubling the dose from 2 to 4 mg/kg
(no change in elimination processes) will only increase the teff
to 3.98 hours, an increase of 22.8%.

28. EFFECT OF ELIMINATION HALF LIFE ON
DURATION OF ACTIVITY
The effect of prolonging the elimination half-life has an
extremely important effect on the treatment of infections,
particularly in patients with high metabolism, or clearance,
of the antibiotic.
Therefore, antibiotics must be dosed with full consideration
of the effect of alteration of the t1/2 on the teff.