Half-Life

Question 1

Define half life

Answer 1

Half-life is the time taken for the amount of drug in the body (or the plasma concentration) to fall by half

Question 2

Compare first order and zero order kinetics. Give examples of drugs that are eliminated by zero order kinetics

Answer 2

First-order kinetics: a constant FRACTION of a drug is eliminated per unit of time

• -> Concentration-dependent process
• -> Graph [drug] : time –> exponential washout curve
• -> log y-axis: straight line with -‘ve gradient

Zero-order kinetics: a constant AMOUNT of a drug is eliminated per unit time

• -> Concentration independent process
• -> Graph [drug] : time –> straight line
• -> E.g. Ethanol, phenytoin, salicylates (Non-linear kinetics)

Question 3

What is Michaelis-Menton kinetics. Write the Michaelis-Menton equation. What does the enzyme reaction rate - drug concentration graph for non-linear kinetics look like?

Answer 3

Describes enzymatic reactions where a maximum rate of reaction is reached when drug concentration achieves 100% enzyme saturation.

V = Vmax x [S]
________
Km + [S]

V - rate of reaction
Vmax - Maximum rate of reaction
[S] - substrate or drug concentration
Km - ‘K’oncentration at 50% of Vmax

Question 4

What is meant by non-linear elimination kinetics? Give examples of drugs cleared by non-linear elimination kinetics

Answer 4

Drug clearance by Michaelis-Menton processes, where a drug at low concentration is cleared by first order kinetics and at high concentrations by zero order kinetics. E.g. phenytoin / ethanol

Question 5

How can you predict the concentration of a drug at a certain time after it has been administered given that the drug undergoes first order elimination kinetics

Answer 5

If a drug is eliminated by first order kinetics, its concentration falls by some sort of elimination rate constant, which is usually expressed as a fraction cleared per unit time (e.g. 0.1/hour or 10% per hour)

When plotted on a semilogarithmic scale, the exponential washout curve becomes linear. With this linear predictability, the following equation can be used to estimate the concentration C of the drug at any given time t.

C = Co x e^-kt

C - concentration of drug
Co - concentration of drug at time = 0
-kt - elimination rate constant, as a fraction per unit time

Question 6

How does half life relate to the elimination rate constant in first order kinetics

Answer 6

k = 0.693
___
t1/2

k - elimination rate constant as a fraction per unit time

t1/2 - Half-life

0.693 is natural logarithm of 2
(we use the natural logarithm of 2 because we are dividing by 2 –> i.e. half life not ‘tenth-life which would be natural logarithm of 10)

Question 7

How does half life relate to the volume of distribution and the clearance of a drug

Answer 7

k = Cl
__
Vd

elimination rate constant is proportional to clearance but inversely proportional to volume of distribution. This is because drug can’t be cleared if it is bound to proteins or fat inside tissues, i.e. not in the plasma. If drug is not in the plasma then it can’t flow through and organ (liver/kidney/lung/dialysis machine) to be cleared.

Therefore,

t1/2 = 0.693 x Vd
________
Cl

t1/2 = half life
0.693 = ln 2
Vd = Volume of distribution
Cl = clearance

Question 8

Is t1/2 similar to clearance

Answer 8

No. Its relationship with volume of distribution makes it a poor surrogate for clearance