2. Dose–Response Relationships
The pharmacodynamics of a drug can be quantified by
the relationship between the dose (concentration) of
the drug and the organism's (patient's) response to that
2 major types of dose–response relationships—graded
Graded dose–response relationships describe the
effect of various doses of a drug on an individual.
Quantal dose–response relationships show the effect
of various doses of a drug on a population of individuals.
4. ……Graded dose–response relationships
Two important parameters—potency and efficacy
The potency (EC50) of a drug is the concentration at which
the drug elicits 50% of its maximal response.
The efficacy (Emax) is the maximal response produced by the
No inter-individual variation.
5. Quantal Dose–Response Relationships
Plots the fraction of the population that responds to a given
dose of drug as a function of the drug dose.
The response is all-or-none.
Differences in biological response among individuals - the
effects of a drug are seen over a range of doses.
Flat curve denotes a broad range of sensitivity, a steep one
denotes a very narrow range
6. …….Quantal Dose–Response Relationships
Types of responses:
Median effective dose (ED50): dose at which 50% of
subjects/animals exhibit a therapeutic response to a drug.
Median toxic dose (TD50): dose at which 50% of subjects
experience a toxic response.
Median lethal dose (LD50): dose at which is lethal to 50% of
8. …….Quantal Dose–Response Relationships
Values are different for each route of administration.
Both LD50 and ED50 values are important for knowing the
safety of a drug.
The ratio between LD50 and ED50 (LD50/ED50) represents
Greater the TI, safer is the drug and vice-versa.
9. …….Quantal Dose–Response Relationships
The TI of most of the drugs which have low margin of
safety is generally close to unity.
ED99 dose that is effective in 99% of the animals of the
LD10 dose that is lethal to 10% of the animals of the group.
LD50 and ED50 are mainly determined in acute toxicity
10. Acute Toxicity Studies
Acute toxicity refers to those adverse effects occurring
following oral administration of a single dose of a
substance, or multiple doses within 24 hr.
Aims at establishing the therapeutic index (TI)
Several species of animals are used to determine LD50
(due to species variation)
A drug effect seen both in the rat and dog probably
involves a common physiological mechanism that is
likely to be present in the human, whereas an effect
seen only in one of the two species indicate that the
same is peculiar to that species, and is less likely to be
present in the third species.
11. ……..Acute Toxicity Studies
In practice, it is considered sufficiently adequate if LD50
with confidence limits is established on one common
laboratory species, mice or rats by the standard method.
It is unwise to use a homogenous strains (inbred strains) in
toxicity study, and the aim should be to discover new and
unexpected effects of a drug in animals of wider variability
like random bred animals.
LD50 dose, thus found is then given to guinea pigs, rabbits,
cats or dogs on the basis of their weight or surface areas.
12. Requirements of a toxicity study
Should follow GLP
Studies should be performed by well trained and
Instruments should be calibrated and standardized
SOPs should be followed.
13. Acute Toxicity Test Design
First performed in mice fasted overnight (18hours)
Two rodents species(mice and rats); in each group at least 5
animals of either sex.
Route of administration-
• Same as intended for humans.
• At least one more route should be used in one of the species
to ensure systemic absorption of the drug.
• LD50 values increase with the following sequences of
routes: intravenous, intraperitoneal, subcutaneous and oral.
14. ……Acute Toxicity Test Design
At least three graded dose. A limit of 2g/kg (or 10 times
the normal dose that is intended in humans, whichever is
higher) is recommended for oral dosing.
Treatment- given in a single bolus or several doses or by
continuous infusion within 24 hr.
In rodents, the volume should not normally exceed
1ml/100g of body weight; however in the case of aqueous
solutions, 2 ml/100g body weight can be considered.
15. ……Acute Toxicity Test Design
Animals should be observed for 14 days after the drug
administration, and minimum lethal dose (MLD) and
maximum tolerated dose (MTD) and LD50 should be
established. Other features to be observed are-
Signs of intoxication
Effect on body weight
Gross pathological changes
16. ……Acute Toxicity Test Design
Each dose given to one animal only
LD50 estimated from mean of the logarithms of the smallest
effective dose and the largest ineffective dose.
Up and down’ or ‘staircase’ method
First described by Dixon and Mood.
2 mice injected with a particular dose, eg: 175mg/kg
17. ………Up and down’ or ‘staircase’ method
Observe for 48 hours
Dose tolerated- increase by a factor of 3.2
Dose lethal- decrease by a factor of 3.2
Maximum nonlethal dose and minimum lethal dose are thus
determined by using only about 10 mice
Economical in animal but not in time
19. Kärber's method
Based on the “S” shaped dose-response curve
The drug dosage are arranged by geometric progression
60 mice weighed, divided into 6 groups randomly, 10 mice
per group. Average weight of each group should be roughly
Geometric proportion diluents made according to the
Mice observed for 30-50 minutes after administration.
Mice showing response counted.
Positive reaction rate of each group calculated.
Table filled with the results.
21. ……Kärber's method
• ED50 calculated by the formula:
• Where, Xk=logarithm of the maximum dosage.
• i=logarithm of the ratio of the adjacent doses.
• is the sum of the positive rate of each group. P1,P2,P3,……
is the positive rate of each group.
22. Methods for calculating LD50
Lichtfield and Wilcoxon (1949) - Graphical method
L.C Miller and Tainter (1944) – Logarithmic probit graph
De Beer (1945) – Graphical method
Reed and Muench (1938) – Arithmetical method
Kärber (1931) – Arithmetical method
23. Graphical calculation of Lichtfield and
Permits rapid estimation of LD50, slope of a dose-
percent effect curve, and the confidence limits of
both parameters for 19/20 probability using the
experimental data in their original form.
Graphical calculation of L.C Miller and Tainter
Most commonly used method
Acurate and simple
Percentage mortality noted in the groups of animals
27. Correction factor applied to 0 and 100% mortality group
Correction for 0% dead = 100(0.25/n)
Correction for 100% dead = 100×(n-0.25/n)
Percentage mortality values converted to probit
(Probability integral transformation) values.
The log dose is plotted in X- axis.
Probit scale is plotted in Y-axis.
The LD50 is equal to the antilog dose corresponding to
probit 5 (50%)
In this example, the value is antilog of 1.9, i.e.,
28. Arithmetical method of Kärber (1931)
No dose response curve
Simplest, rapid but crude method
Use the interval mean of the number dead (Mean mortality)
in each group of animals and the difference between the
doses (dose difference) for the same interval
Mean mortality= total of two adjacent no of dead animal/2
e.g. (0+2) /2 = 1
Dose difference e.g. 71-64= 7
29. …..Arithmetical method of Kärber
Product of the interval mean and the dose difference is
obtained (a×b) e.g 7×1=7
The product is summed up i.e., Ʃ (a×b) = 190.5
Now dividing the value by no of animals in each group =
190.5/10 = 19.05
Finally this value is subtracted from the minimum dose
which produces the 100% mortality, i.e. 100 mg/kg
So, LD50 = 100-(190.5/10) = 81 mg/kg (approx)
31. Arithmetical method of Reed and Muench (1938)
Employs a cumulative value.
Less reliable than Miller and Tainter method.
Animals killed by a certain dose would have been killed
by a larger dose
A surviving animal would have survived a smaller dose
32. Table: Toxicity computed by Reed and Muench Method
Group Dose Dead Survived Dead Survived Total
1 100 10 0 10 25 35
2 90 9 1 19 25 44 -
3 81 4 6 23 24 47 51.1
4 71 2 8 25 18 43 41.9
5 64 0 10 25 10 35
34. ….Reed and Muench Method
The cumulative dead are recorded
The cumulative survivors are recorded upward
% survival for both doses adjacent to the LD50 is computed
Proportionate distance from 50% is computed
Logarithm of the proportionate dose increment computed
35. ….Reed and Muench Method
Proportionate distance from 50% X logarithm of the
proportionate dose increment.
This is added to the logarithm of the smaller adjacent dose
to form log LD50.
Antilog of the above value gives LD50.
36. Lorke’s Method
Three-groups of three mice each.
One dose to each group i.p.
Monitored for 24 h for mortality and general behaviour.
3–4 groups of one mouse each given doses i.p. based on the
findings of phase 1
Monitored for 24 h.
The geographic mean of the least dose that killed mice and
the highest dose that did not kill mice was taken as the
median lethal dose.
For many reasons TI is not a useful guide to safety
of a drug in clinical use:
LD50 based on animal toxicity data, may not
reflect toxicity in the therapeutic setting ,where
unwanted effects are rarely common but not
LD50 takes no account of idiosyncratic reactions.
ED50 not definable, depends on what measures of
effectiveness is used.