DRC , QUANTAL DRC , GRADED DRC,THERAPEUTIC INDEX , SUMMATION CUMMULATION TOLERANCE

1. Dose Response Relationship
Wide quantitative variations in drug responses can occur between different species and
within the same species under different conditions. Methods have, therefore, been devised
to study the phenomenon of variation in pharmacological drug response and to minimise
the errors of prediction in therapeutic use of drugs.
Each drug has a characteristic dose response curve for a specified set of conditions, but
in general, the dose response curve confirms to the S-shaped or sigmoid type, or to
segments of the sigmoid.
The magnitude of the drug effect is a function of the dose
administered. Two basic types of dose effect relationship have been observed:
(i) Graded or quantitative dose-response relationship; and
(ii) Quantal or all or none dose-response relationship
Graded or quantitative dose-response relationship: This type of relationship relates the
size of the response in a single biological unit to the dose of the drug. As the dose
administered to a single subject or discrete organ or tissue is increased, the
pharmacological response also increases in graded fashion provided the dose has exceeded
some critical level called the Threshold dose . The graded dose-response relation is
partially a reflection of the extent of occupancy of the receptors by the drug. Since an entire
dose response relationship is determined from one animal, the curve does not tell us about
the degree of biological variation inherent in a population.
Effect of graded dose of histamine on isolated guinea-pig ileum.

2. The degree of response produced by increasing doses of a drug eventually reaches a steady level,
termed as the ceiling response, and the dose with which it is obtained is the ceiling dose. If the
dose exceeds the ceiling dose, there is no further increase in the therapeutic effect.
In fact, such a dose may provoke different and possibly undesirable
responses. The ceiling dose allows us to compare the therapeutic efficacy of various
compounds.
The latter is particularly useful for the
comparison of various compounds.
Dose-response relationship curve from the data in
Same dose-response relationship plotted on logarithmic scale.

3. Quantal or all or none dose-response relationship: In contrast to graded responses, the
quantal responses are all or none. The quantal curve shows the frequency with which any
dose of a drug evokes a stated, fixed (all or none) pharmacological response in a subject
population. It is, therefore, essentially a frequency distribution of the responders (actual
numbers or percentage of the total number of subjects) to different doses of the drug.
Each subject is categorised as responding or non-responding, according to a prior decided
criterion of response.
While studying an anti-epileptic drug in animals, each animal is
classified as responding (seizure-free) or not responding at a specified time after the drug
treatment. Obviously, sensitive animals will respond to smaller doses while some will be
resistant and need very large doses. Usually, the sensitivity of animals to different doses is
distributed normally with respect to the logarithm of the dose. Thus, for a given drug, if
log dose is plotted on the horizontal axis and the % responding to the various dose levels is
plotted on the vertical axis, a Gaussian (normal) distribution is obtained .
The curve represents the distribution of sensitivity of a group of animals to the given drug. In
this figure about 10 % of the animals in a given population remain seizure-free at a dose level of
log dose ‘0’, while another 10 % do not respond until the dose is increased to log dose ‘2’.
Majority of the animals, however, respond at doses between ‘0.5’ and ‘1.5’ on the
log scale. The same data, plotted as the cumulative number of animals that responded
against log dose, would give an S shaped cumulative frequency curve.
For a given dose of a drug, a cumulative frequency curve gives the per cent of animals
responding to that dose and to lower doses.
Quantal dose response curve

4. The quantal dose response curve, however, is not always exactly symmetrical or bell-shaped
but may show ‘skewing’ or ‘truncation’. This shows that besides polygenic random
variation, non-random but inter-coupled events like other actions of the drug and
experimental limitations influence the quantal dose response curve.
Therapeutic Index:
Therapeutic index (TI) : It is an approximate assessment of the safety of the drug. It is
expressed as the ratio of the median lethal dose to the median effective dose.
Effective Dose:
The median effective dose or ED50 : This is the dose (mg/kg) which produces a desired
response in 50 per cent of the test population.
The quantal dose–response curve represents estimates of the frequency with which each dose
elicits the desired response in the population. In addition to this information, it also would be
useful to have some way to express the average sensitivity of the entire population to
phenobarbital. This is done through the calculation of an ED50 (effective dose, 50%; i.e., the
dose that would protect 50% of the animals). This value can be obtained from the dose–response
curve.
The ED50 for phenobarbital in this population is approximately 4mg/kg.
Lethal Dose:
The median lethal dose or LD50 : This is the dose (mg/kg) which would be expected to
kill one-half of an unlimited population of the same species and strain.
Another important characteristic of a drug’s activity is its toxic effect. Obviously, the ultimate
toxic effect is death. A curve similar to that already discussed can be constructed by plotting
percent of animals killed by phenobarbital against dose.
From this curve, one can calculate the LD50 (lethal dose, 50%). Since the degree of safety
associated with drug administration depends on an adequate separation between doses
producing a therapeutic effect (e.g., ED50) and doses producing toxic effects (e.g., LD50), one
can use a comparison of these two doses to estimate drug safety. Thus, one estimate of a drug’s
margin of safety is the ratio LD50/ED50; this is the therapeutic index.
The therapeutic index for phenobarbital used as an anticonvulsant is approximately 40/4,or 10 .

5. As a general rule, a drug should have a high therapeutic index; however, some important
therapeutic agents have low indices. For example, although the therapeutic index of the cardiac
glycosides is only about 2 for the treatment and control of cardiac failure, these drugs are
important for many cases of cardiac failure.
Therefore, in spite of a low margin of safety, they are often used for this condition.
The identification of a low margin of safety, however, dictates particular caution in its use; the
appropriate dose for each individual must be determined separately.
It has been suggested that a more realistic estimate of drug safety would include a comparison of
the lowest dose that produces toxicity (e.g., LD1) and the highest dose that produces a maximal
therapeutic response (e.g., ED99).
A ratio less than unity would indicate that a dose effective in 99% of the population will be lethal
in more than 1% of the individuals taking that dose. Figure indicates that Phenobarbital’s ratio
LD1/ED99 is approximately 2.
The margin of safety is the difference between the therapeutic and the lethal doses.
As the drug metabolism varies from species to species, the TI would also vary.
Therapeutic index supplies reliable information when both the LD50 and ED50 are
determined for the same strain of a given species. ED50 can be obtained from either
quantal or graded dose response curves.
As LD50 cannot be worked out in humans, the formula for TI in humans can be restated
as:
The larger the TI, the safer is the drug. For safe therapeutic application of a compound, its
TI must be more than one. Such drugs have very little dose-related toxicity. Thus, penicillin
has a very high TI while it is much smaller for digoxin, aminophylline and lidocaine.
In practice, no drug produces only a single effect but has a spectrum of effects. Further,
a drug may be selective in one respect but nonselective in another. Thus, although
antihistaminics selectively block histamine actions, most of them cause significant
sedation.
For therapeutic purposes, selectivity of a drug effect is clearly one of its more
important properties. Thus depending upon its effect, a drug may have many therapeutic

6. indices.
Example: The margin of safety of aspirin when used for headache is far greater than its
margin of safety for the relief of arthritic pain or in rheumatic fever. This is because the
latter use requires much larger doses.
In clinical practice, there is often a need to use two or more drugs concurrently. The
resultant effect may vary depending on the combination used. There may be:
(1) Additive effect (Summation):
When the total pharmacological action of two or more drugs administered together is
equivalent to the sum of their individual pharmacological actions (1+1=2), the phenomenon
is termed as an additive effect e.g. combination of aspirin and paracetamol in the
treatment of pain and fever.
(2) Synergism:
Facilitation of a pharmacological response by the concomitant use of two or more drugs
is called drug synergism. The word synergism is derived from the two Greek words, ergo
(work) and syn (with) and indicates a pharmacologic co-operation. This co-operation
usually results in a total effect greater than the sum of their independent actions (1+1>2),
e.g. codeine and aspirin for pain; hydrochlorothiazide and atenolol for hypertension.
If the synergism results in prolongation of action of one of the drugs, it is termed time
synergism, e.g. procaine and adrenaline combination increases the duration of action of
procaine. The term potentiation is often loosely employed for synergism and should be
avoided, as the word ‘potentiate’ means ‘to endow with power’, which no drug is really capable
of achieving.