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KINETICS OF PHARMACOLOGICAL RESPONSES

 

Assumption:

• Direct effect.

• Reversible action.

• Metabolites inactive.

• Tolerance does not develop.

Under these assumptions, the quantification of pharmacological response produces the familiar log dose - response curve, with an almost linear relationship between the log dose and the response within the range of 20 to 80% of maximum intensity of effect.

(a) Time Course of Pharmacological Response:

	E	=	m log C	+		e
	Intensity of effect		slope			intercept
		..
	log C		E - e
		=	________
			m
		..
		=			kt
			log Co -		________
					2.303
		..
	E - e	=	Eo -e				-	kt		where log Co =	Eo - e
	________		________					________			________
	m		m					2.303			m
		..
	E	=	Eo -		kmt
					________
					2.303

Hence, the intensity of effect decreases at a constant (zero order) rate RE, which is a function of the apparent first-order constant (k) and the slope of the effect versus log C curve (m).

Ie.  RE		km
	=	_____
		2.303

For a large number of drugs, the loss of effect is essentially linear over a very wide response range.

Discrepancies between time course of response and plasma drug concentrations:

Eg. Beta blockers : t½ short (~ 4 hrs), but can dose daily or bd in hypertension. Give large doses to exceed 80% response point - by end of dose interval, the plasma level has dropped markedly. However, the effect has decreased relatively little.

NB: Only during the period when drug concentrations are in the steep portion of the concentration response curve (20-80%) does any appreciable reduction in response with time occur.

 

(b) Duration of Response:

Assume that the intensity of response Ab

Ab = minimum amount of drug in body necessary to produce an effect.

Then log Ab			k td
	=	log Ab -	_____
			2.303

Where 

Ab = Initial amount in body (= IV dose)
td = Duration of effect.

	2.303 log Ab	-	2.303 log Ab
td =	_____________		_____________
	k		k

NB can increase td by Ab (explains discrepancies with B-blockers, etc).

td increases linearly as dose size increases logarithmically ( need very large dose increase to usefully prolong td).

Need to balance risk of dose versus benefit of td.

 

(c) Complex Response Situations:

(i) Slow equilibration with site of action:

Eg. Digoxin : good correlation between drug tissue (myocardial) concentration and intensity of response.

NB Only after ~ 6 hours is there any constant relationship between plasma and tissue concentrations of Digoxin and therefore between plasma Digoxin levels and response.

plasma samples of Digoxin should always be drawn > 6 hours post-dose.

(ii) Active Metabolites:

Eg. B-blockers

(iii) Indirect pharmacological effects:

Eg. Warfarin.

Inhibits the synthesis of Vitamin K - dependent clotting factors (II, VII, IX, X).

However, the anticoagulant response is a function of both the synthesis and degradation of the factors.

See a delayed response in prothrombin time.

he measured response is not the direct pharmacological effect of Warfarin.

The direct effect is the inhibition of synthesis of the Vitamin K - dependent factors.