# Intensity of Effect-Concentration Relationships

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## Chapter: Biopharmaceutics and Pharmacokinetics : Drug Concentration and Pharmacological Response

In case of a drug that produces quantal response, the pharmacodynamic parameter that correlates better with its concentration is duration of action.

### Intensity of Effect-Concentration Relationships

In case of a drug that produces quantal response, the pharmacodynamic parameter that correlates better with its concentration is duration of action. The parameter intensity of response is more useful for correlation with the concentration of a drug that shows graded effect. Like duration of action, intensity of action also depends upon the dose and rate of removal of drug from the site of action. The intensity of action also depends upon the region of the concentration-response curve (refer Fig. 13.1). If a drug with rapid distribution characteristics is given as i.v. bolus dose large enough to elicit a maximum response, the log concentration-response plot obtained will be as shown in Fig. 13.1. The relationship between dose, intensity of effect and time can be established by considering the plots depicted in Fig. 13.5. which also shows 3 regions.

Fig. 13.5 The fall in intensity of response with drug concentration and with time following administration of a single i.v. bolus dose.

Region 3 indicates 80 to 100% maximum response. The initial concentration of drug after i.v. bolus dose lies in this region if the dose injected is sufficient to elicit maximal response. The drug concentration falls rapidly in this region but intensity of response remains maximal and almost constant with time.

Region 2 denotes 20 to 80% maximum response. In this region, the intensity of response is proportional to log of drug concentration and expressed by equation 13.2.

Intensity of Effect = P log C + I               (13.2)

Since the decline in drug concentration is a first-order process, log C can be expressed as:

Substituting 13.8 in equation 13.2. and rearranging we get:

If Eo is the intensity of response when concentration is Co, then:

Equation 13.10 shows that the intensity of response falls linearly (at a constant zero-order rate) with time in region 2. This is true for most of the drugs. The drug concentration however declines logarithmically or exponentially in region 2 as shown by equation 13.8.

Region 1 denotes 0 to 20% maximum response. In this region, the intensity of effect is directly proportional to the drug concentration but falls exponentially with time and parallels the fall in drug concentration.

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