Pharm - Exponential Functions

Question 1

Draw a graph to show how the concentration of a drug administered intravenously varies over time

Answer 1

Concentration=change in drug concentration/change in time

Question 2

What is an exponential function?

Answer 2

It describes how the rate of change is proportional to the quantity of substance at that time.

Plasma concentration= concentration at time zero x e^ -kt

E= base of natural log (Euler’s number=2.72)
K= rate constant
T= time

Question 3

What are the properties of an exponential decay curve?

Answer 3

1. Plasma concentration approaches but never touches 0 (i.e. reaches the asymptote - in approx 5 half lives or 3 time constants)
2. Whilst the amount of drug eliminated per minute varies, the proportion of drug eliminated per minute is constant
3. The rate of decline in drug concentration is proportional to drug concentration at that time point
4. The gradient of the curve is K=elimination rate constant

Question 4

Examples of exponential processes

Answer 4

Decay curves:
Nitrogen washout during pre-oxygenation
Lung volumes in passive expiration
Drug wash-out curves
Radionuclide materials undergoing decay

Growth curves:
Bacterial growth
Lung volumes in positive pressure ventilation
Drug wash-in curves

Question 5

Draw the log concentration-time curve
Why do we use this?
What does it tell us?

Answer 5

Log of the concentration in a semilogarithmic plot (time is not logged) provides a straight line from which values can be derived.
These include:

*K= elimation constant - the rate of change in plasma concentration per unit time
*T(tau)= time constant - the time it would take for plasma concentration to reach zero if it had the original rate of change (reciprocal of K), also the time taken for the concentration to fall to 37%
*C0= concentration at time 0
* T1/2= half life, the time taken for plasma concentration to fall by half. =0.693(Tau) or 0.693/k
*Vd= volume of distribution is the theoretical volume that a drug must disperse into to produce the measured plasma concentration. Vd=dose/C0
*Cl=clearance which is the volume of plasma completely cleared of a drug per unit time. Cl=Vd x k

Question 6

Reference card of logarhithm rules

Answer 6

• So, the logarithm of a number is the power to which the base would
  have to be raised to equal that number.
  E.g. for base 10, log of 100 = 2
• We also use the ‘natural logarithm’, whose base is referred to as ‘e’.
• e = 2.718 (approximately).
• So, the natural logarithm of number X is the power to which e
  would have to be raised to equal X

When using logarithms:
* Multiplication becomes addition
log (ab) = log (a) + log (b)
* Division becomes subtraction
log (a/b) = log (a) – log (b)
* Power becomes multiplication
log (a^b) = b.log(a)
* Reciprocal becomes negative
log (1/a) = – log(a)