Pharmacodynamics - Dose-response relationships

Dose-Response Relationships

The response to a drug varies according to its dosage i.e. the magnitude of the drug effect is a function of the dose administered. The relation between the responses produced by different doses is expressed by graphical representation called dose response curves. Two forms of dose-response curves are recognized: 1.Graded response & 2.Quantal response

1. Graded dose response: It is the one in which the target tissue or even patient shows a progressively greater response with increasing doses of drug, ultimately reaching the maximum response. A plotted graph of a graded response is hyperbola on a linear scale and a sigmoid curve on semi-logarithmic scale. Graded dose response curve gives the relation between dose of the drug and intensity of the response in a single biological unit.

This curve depicts the

1) Threshold dose - The minimum dose at which observable changes arc noticed.

2) Ceiling dose - The minimum dose producing the maximal response and any further increase in the dose above the ceiling dose will not increase the level of response.

3) Potency – this refers to the dose (concentration) of a drug needed to produce an effect smaller the dose to produce the effect, the greater the potency. Potency is not an important property of a drug, provided the dosage form of the drug can be conveniently administered. If two drugs have similar pharmacological activities, the more potent drug is not necessarily the drug of choice. Consideration must also be given to other factors such as side effects, toxicities, cost and duration of action.

4) Slope - It is of both practical and theoretical importance. Slope represents the change in response to the change in dose of drugs. Drugs that have steep DRCs are potentially more difficult to use because small increase in the dose may produce toxity. Drugs that act on common receptor have DRCs with parallel slopes.

5) Variability - The Variability in the response can be related to the variation in dosage.

6) Maximal effect - is the maximum response possible for the effector.

Graded dose response curve is considered as a plot of efficacy Vs drug concentration. By plotting this we can calculate:

EC50: The drug concentration at which 50% efficacy is attained. The lower the EC50, the more potent the drug.

Emax: The maximum attained biological response out of the drug.

2. Quantal dose response: This is also known as All or none response. In this, the target tissue or patient, reacts either maximally or to a specific end point with in the therapeutic dose range. This represents the % response of animals in a group of population to the doses of the drug. The quantal D-R curve relates dose to an expression of the frequency with which any dose of the drug produces an all or none pharmacologic effect.

Each animal receiving a dosage is categorized as responding / non-responding.  The % responding to each dose are recorded (i.e. % alive, % dead, % responded or % not responded). These quantal responses (%) when plotted against log doses they do not show a linear regression. However when % is transformed into probits, the relationship becomes linear. This type of curve is used for estimating ED50/LD50 values of a drug.

Quantal DRC is a graph of discrete (yes/no) values, plotting the number of subjects attaining the condition (such as death or cure from disease)  vs drug conccntration.

ED50 - The drug dosage at which 50% of the population attains the desired characteristic.

LD50 - The drug dosage at which 50% of the population is killed by a drug.

Therapeutic index: It is the ratio used to evaluate the safety of the drug. TI = LD50 / ED50. Larger the TI, the safer the drug. i.e. the higher dose is required for lethality, compared to the dose required to be effective. However, if the LD50 and ED50 curves are not parallel, the TI may be misleading.

Margin of safety: This is the ratio of dosage required to kill 1% population, compared to the dosage i.e. effective in 99% of population. Margin of safety = LD1/ED99.

Standard safety margin: It is the per cent by which the ED99 must be increased before an LD1 is reached.

SSM = [(LD1- ED99) / ED99] x 100

Therapeutic ratios are also useful indices of drug safety but in this case the steepness of the dose response curves are taken into consideration. Therapeutic ratios are often calculated by dividing the LD25 by the ED75.