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PHARMACOKINETICS

 

Pharmacokinetic Models:

• Oversimplified but useful mathematical models for describing the pharmacokinetic behaviour of a drug in the body.
• Depict the body as a single compartment or a series of compartments.
• These compartments do not necessarily have any anatomical or physiological reality.

Can be most readily applied to drugs that rapidly distribute between blood and tissue after absorption.

2. Two-Compartment Model:

Often too complex for clinical applications.

Transfer of drug from the administration site to the systematic circulation.

(a) Barriers of Absorption:

(R&T Page 12).

(b) Mechanisms of Absorption:

1. Passive Diffusion:

Most drugs.

2. Active (Carrier-medicated) Transport:

Eg. Levodopa.

(c) Bioavailability (Refer to Biopharm Notes):

1. Rate of Absorption:

• Important for rapid onset of effect.

Methods for Estimating Rate of Absorption:

- Time of peak plasma level (tp).

- Determine ka - Method of residuals.

- Percent of unabsorbed - For plots

(Large ka - rapid absorption).

 

2. Extent of Absorption:

Absolute Vs relative bioavailability.

Methods for Estimating Extent of Absorption:

Plasma levels

F=	AUC
	__________________
	AUC

Eg. trapeziodal role (R&T page 288).

 

Urinary recovery (if largely excreted unchanged).

F=	Xu
	__________________
	Xu

(Xu = total amount of unchanged drug excreted in urine).

Eg. 

Drug	F (oral) %
Ampicillin	50
Digoxin	50-90
Warfarin	100
Penicillin G	<30
Doxycycline	100

(d) Factors Influencing Bioavailability:

Refer to Biopharm notes.

Reversible transfer of drug from one site to another within the body.

(a) Apparent Volume of Distribution (Vd):

Simply a proportionality constant

Vd =	Ab
	______
	C

The size of a compartment necessary to account for the total amount of drug in the body if it were present throughout the body in the same concentration found in plasma.

Drug	Approx VD (L)
Warfarin	7
Theophylline	35
Phenytoin	40
Nortriptyline	300
Digoxin	500

(b) Factors Influencing Distribution:

(i) Blood flow to tissue:

Blood Flow Under Basal Conditions and the Relative Size and Water Content of Different Organs and Tissues¶
Organ	Percent of Body Volume	Percent Water	Blood Flow (ml/min)	Percent of Cardiac Output	Perfusion Rate (ml/min/ml of tissue)	Relative Perfusion Rate§
1. Adrenal Glands	0.03	--	25	0.2	1.2	17
2. Blood	7	83	(5000)¤	(100)	--	--
3. Bone	16	22	250	5	0.02	0.3
4. Brain	2	75	700	14	0.5	7
5. Fat	10	10	200	4	0.03	0.4
6. Heart	0.5	79	200	4	0.6	8
7. Kidneys	0.4	83	1100	22	4	55
8. Liver Portal Arterial	2.3	68	1350 (1050) (300)	27 (21) (6)	0.8	11
9. Lungs	0.7	79	(5000)	(100)	10	140
10. Muscle	42	76	750	15	0.025	0.35
11. Skin (Cool weather)	18	72	300	6	0.024	0.35
12. Thyroid Gland	0.03	--	50	1	2.4	34
TOTAL BODY	100	60	5000	100	0.071	1.0
¶ Compiled from data of Guyton, A.C.: Textbook of Medical Physiology, 5th ed. W.B. Saunders, Philadelphia, 1976. p.251; and Skelton, H: The storage of water by various tissues of the body. Arch. Intern. Med., 40: 140-152, 1927. Copyright 1927. America Medical Association. § Perfusion rate relative to the average perfusion rate of the whole body. ¤ Values in parentheses given for comparison.

 

(ii) Lipid Solubility:

Generally high lipid solubility implies high Vd, eg. Thiopentone.

“Blood-brain” barrier.

Distribution into fat and dosing in obese patients, eg. Digoxin.

 

(iii) Regional Differences in pH:

Eg. Breast milk (acidic pH).

(iv) Binding:

Plasma Protein Binding:

Acidic drugs often bind to albumin.

Basic drugs - Glycoprotein and Lipoproteins.

Generally, high plasma protein binding implies low Vd:-

Drug	% Bound	VD (L)
Warfarin	99	7
Phenytoin	90	40
Digoxin	30	500

NB Changes in binding will influence distribution

Eg Hypoalbuminaemia
Renal failure
Drug displacement interactions.

Tissue Binding:

Generally, high degree of tissue binding implies large Vd, eg. Digoxin.

Vd =		fu	(R&T Page 44)
	V + V .	______
		fu

 

 \Vol is dependent both on plasma protein binding and tissue binding as :

fu , Vd

fu, Vd

Irreversible loss of drug from the body:

(a) Metabolism, and

(b) excretion of unchanged drug.

Clearance (Cl):

Theoretical volume of plasma which is cleared of drug per unit time (ml/min).

Cl =	Rate of elimination
	__________________
	Plasma concentration

 

Total body clearance

=  Renal Clearance (Cl)

+

Hepatic Clearance (Cl)

+

Clearance by other routes

Half-life:

t½ =	0.693 Vd
	__________
	Cl

(or Cl - k . Vd)

Extraction Ratio: (R&T Page 49)

	Ca	Organ of Elimination	Cv
Q

 

E  =	Ca - Cv
	__________		(0 - 1)
	Ca

 

Rate of extraction		=	Q. (Ca - Cv)
..		.
Now,	Cl	=	Rate of elimination
			____________________
			Concentration
.	.
Cl		=	Q. (Ca - Cv)
			_______________
			Ca
.
		=	Q . E

 

High extraction ratio (~1)	Low extraction ratio (< 0)
Cl Q as Q, Cl (flow restricted)	Cl E (flow independent)

NB Blood clearance, rather than plasma clearance

Cl plasma	=	C blood
________		________
Cl blood		C plasma

Renal Excretion:

Drugs excreted largely unchanged by the kidney

Amantadine	Cimetidine	Nadolol
Aminoglycosides	Cisplatin	Penicillins
Atenolol	Digoxin	Procainamide
Baclofen	Ethambutol	Sotalol
Bendrofluazide	Flucytosine	Tetracycline
Bleomycin	Frusemide
Bretylium	Guanethidine
Bumetanide	Hyoscine
Cephalosporins	Lithium
Chlorothiazide	Metformin
Chlorpropamide	Methotrexate

 

 

(a) Glomerular filtration:

RBF ~ 1.2-1.2 l/min

~ 10% is filtered at glomerulus, ie. GFR ~ 125 ml/min

Only unbound (free) drug

If no reabsorption or secretion occurs,

ClR	=	Rate of excretion
		__________________________
		Plasma Concentration
.	.
	=	GFR . Cu
		_______________
		C
.
		GFR . Fu

Creatinine clearance.

 

(b) Active secretion:

 If ClR > GFR, then active secretion must occur.

Acids (eg. Penicillins) and bases (eg. Procaine).

Independent of plasma protein binding.

Competition can occur (eg. Probenecid - Penicillins).

(c) Reabsorption:

Passive diffusion.

Unionised drug.

pKa and urine pH important for weak acids and bases.

 

Factors Influencing Renal Clearance:

(a) Renal impairment:

Gentamicin	t½ (hr)
normal	1.5 - 4
anuria	50 - 70

 

(b) Plasma protein binding:

Filtration only

ClR = GFR . fu

Active secretion only

ClR independent of binding

 

(c) Reabsorption of urine pH:

Weak acids:

pKa must lie between 3.0 and 7.5 for ClR to be pH dependent.

Weak bases:

pKa must lie between 6.0 and 12.0 for ClR to be pH dependent.

Pharmacological means of altering urine pH:

• Alkalinise
• Acidify

NB For acids or bases that are very polar when unionised : not reabsorbed regardless of pH, eg. Fobramycin (base)

 

(d) Urine flow:

Extensively reabsorbed drugs as flow, reabsorption and Cl.

---

 

PHARMACOKINETICS

DRUG METABOLISM

Primarily in liver.

NB: Metabolites may be pharmacologically active.

Eg. Diazepam, Pethidine, Sulindac, Prednisolone, Imipramine, Propranolol, Primidone

 

(a) Pathways of metabolism:

Frequently several competing pathways (eg. Salicylate).

 

(b) Hepatic clearance (ClH):

E	=	Ca - Cv
		__________________________
		Ca
..	.
Cl	=	Q . (Ca - Cv)
		_______________
		Ca
.	.
	=	Q . E

Eg.

E
Low	Intermediate	High
Diazepam	Aspirin	Alprenalol
Phenytoin	Quinidine	Lignocaine
Salicylate		Morphine
		Nitroglycerine

 

(c) Factors influencing hepatic clearance:

Age:

Eg.

• Cloramphenicol
• Theophylline

Genetics:

Eg. 

• Acetylator phenotype
• Hydroxylator phenotype

Drug interactions:

Eg. Phenobarbitone

Liver disease:

• Especially chronic (cirrhosis).
• Effects variable.
• No reliable measure of liver function.

Blood flow and plasma protein binding:

nb. Cl = intrinsic clearance = fu . Cl

Cl	=	Q . E
.
	=		Cl
		Q .	______________
			Q + Cl
..	.
Cl	=		fu . Cl
		Q .	______________
			Q + fu . Cl

(i) Drugs with high extraction ratio (or Cl)

Cl Q .	fu . Cl
	________
	fu . Cl
.	.
Cl Q

flow-dependent and not restricted by protein binding (eg. Lignocaine, Propranolol).

(ii) Drugs with low extraction ratio (or Cl)

Cl Q .	fu . Cl
	________
	Q
.
Cl fu .	Cl

Dependent on degree of protein binding (only unbound drug is extracted = “restrictive clearance) and intrinsic clearance of unbound drug.

Eg. Phenytoin, Warfarin, Diazepam

NB. F = L - E

Eg.

Lignocaine E = 0.7; F = .30%

\high E, low F (high first pass effect).

Drug Concentration

Michaelis - Menten description:-

Rate	Vmax . C
	________
	Km + C

 

(i) Low plasma concentrations (Km >> C)

Rate	Vmax . C
	________
	Km

(ie. a first order process)

 

(ii) High plasma concentrations (Km << C)

Rate V max

• Zero order process
• Enzyme saturation
• Only occurs in practice with a few drugs

\drug concentration is only important for drugs displaying saturable kinetics at therapeutic doses (dose-dependent kinetics).