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NON-LINEAR (DOSE DEPENDENT) KINETICS

Rate constants and half-lives do not change with drug concentration.

Non-linear kinetics can occur with any ADME process.

(a) Absorption:

Passive diffusion: first-order (linear) kinetics.

(i) Active transport:

Saturation is possible.

 

(ii) Decreased absorption with high doses of some poorly water soluble drugs:

Eg. Phenytoin, Griseofulvin.

 

(iii) First pass metabolism:

Saturation with high doses leads to increased bioavailability (eg. Propranolol, Hydralazine, Verapamil).

Propranolol: overall extent of absorption by 30% when administered as 40mg bd compared with 20mg qid.

Slow release formulations: overall extent of absorption.

 

(b) Distribution:

(i) Plasma protein binding:

There is a finite number of binding sites for a particular drug on plasma proteins and, theoretically, as the concentration is raised, so too is the fraction unbound (fu).

In practice, significant changes in fu do not occur over a wide range of therapeutic drug concentrations, because the protein concentration >> concentration of most drugs and, therefore, saturation of potential binding sites is not exceeded or even approached.

Exceptions: Eg. Salicylate, Disopyramide, Phenylbutazone, Naproxen, Valproic acid.

Salicylate:

Plasma conc (g/mL)	% Bound
50	96
200	90
800	50

as (Salicylate) , fu and Vd

(ii) Tissue protein binding (distribution into low perfusion tissues):

Saturation of storage sites can occur, eg. Thiopentone, Fentanyl.

With large single bolus doses or multiple dosing, saturation of tissue storage sites can occur ® persistence of drug in central compartment prolonged effects (sedation).

Also, effect of hypothermia.

 

(c) Metabolism (Saturation of Metabolic Enzymes):

Eg.. Phenytoin, Salicylate, Ethanol, Theophylline (especially children).

Michaelis-Menten description

		Vm . C
Rate of metabolism	=	________
		Km + C

Vm = max . rate

Km = concn. at ½ max . rate

 

Low C (Km >> c):

		Vm . C
Rate		________	(first order)
		Km

High C (c >> Km):

		Vm . C
Rate		________	= Vm (zero order)
		C

 

Examples:

(i) Phenytoin:

Calculation of maintenance doses:

(assumes fm 1.0; ie, Cl Clm)

At steady-state, Rate in = Rate out (rate of metabolism)

D		Vm . C
___	=	__________	(Michaelis-Menten)
		Km + C

 

(assuming F 1)

if Vm and Km are known, can calculate D to achieve any Css.

• Population estimates of Vm, Km

Eg. Vm ~ 7mg/kg/day (5-30mg/kg/day)

Km ~ 4mg/L (1-25mg/L)

• Individual patient estimates of Vm, Km

(Need 2 steady-state plasma levels at different dosages).

Eg. “Direct linear plot” method of Mullen.

• Determine Vm and Km from intercepts.
• Can directly read off dose to achieve desired plasma level.

RM is a 32 year old, 80kg male who is being seen in the Neurology Clinic. Prior to his last visit he had been taking 300mg of Phenytoin daily; however, because his seizures were poorly controlled and because his plasma concentration was only 8mg/L, his dose was increased to 350mg daily. Now he complains of minor CNS side effects and his reported plasma Phenytoin concentration is 20mg/L. Renal and hepatic function are normal. Assume that both of the reported plasma concentrations represent steady state and that the patient has compiled with the prescribed dosing regimens. Calculate RM’a apparent Vm and Km and a new daily dose of Phenytoin that will result in a steady state level of about 15mg/L.

(ii) Salicylate:

SU and SPG formation both saturable.

NB: Salicylate - saturable metabolism and protein binding as ­ concentration.

Ie. conc. - fu, Vd

and Cl

Salicylate is a low-extraction drug.

Cl fu x Cl

Cl is unchanged as concn., at least over the therapeutic range.

		0.693 x Vd
But, t½	=	__________
		Cl

t½

(d) Renal Excretion:

Eg. drug partly reabsorbed from tubules by a capacity-limited process: - elimination (excretion) of large doses proceeds more rapidly than with smaller doses, eg. Glucose, Vitamins.

(e) Salicylate Metabolism:

	% Recovery in urine
Aspirin Dose (mg)	SA	SU	SGs
300	2	85	13
1000	7	65	28
2000	25	55	20

 

Aspirin Dose (mg)	Half-Life (Hrs)
300	3
600	4 - 6
1,200	6 - 10
10 - 20g	approx 20

 

Mr Brown, a 58 year old male (72kg), first seen in February 1987 with symptoms of lower respiratory tract infection, was noted to have a lesion in his right lung on Chest X-Ray. Open lung biopsy revealed a carcinoma with metastasis to the axillary lymph nodes. Brain cortical metastasis was demonstrated on CT scan and the patient was started on radiation treatment. Phenytoin therapy was initiated prophylactically at a dosage of 200mg per day. Two weeks later, the patient had a grant mal seizure and the Phenytoin serum level was 5mg/L. The dosage was increased to 300mg per day for an additional two weeks, with three seizures occurring during this period. A serum concentration at the end of this period was 9mg/L (therapeutic range “ 10-20mg/L). What dosage of Phenytoin would be necessary to produce a serum level of 15mg/L?

(10 minutes)