8. Modelling and 2/3 compartment model

Question 1

Why do we use pharmacokinetic modelling?

Answer 1

To predict the behaviour of a drug e.g. change in plasma concentration with time. Need to take ADME into account.

Question 2

What is the only cause of plasma concentration reduction in a one compartment model?

What is the rate of elimination proportional to?

What is this relationship called?

Answer 2

Elimination which is either post-metabolism or unchanged drug.

It is proportional to the plasma concentration and this is called a first order relationship.

Question 3

If a curve is hyperbolic and slopes down with time, what is this called?

When would we see this?

Answer 3

A negative exponential. Y = e (to the power of -x)

When the level of something is reducing e.g. plasma concentration of a drug

Question 4

In a single compartment model, where the rate of a drug being eliminated is proportional to the plasma concentration, whet equation would we use to create an elimination graph?

Answer 4

C = C0e (to the power of -kt)

C = plasma concentration
C0 = concentration at time 0 (mg/ml)
-kt = rateconstant for elimination X time (no units)

Question 5

What are the important elements that need to be considered in a one compartment elimination model?

Answer 5

Input type e.g. bolus or infusion (mg)
Volume of the compartment (ml)
Output e.g. rate of elimination (kt)

C0 = drug given (mg) / Vd (ml) = mg/ml

Question 6

To find the constant of a given drug’s elimination, what do we do?

What kind of graph does this give?

Answer 6

Take the natural log on the elimination equation

InC = InC0 - kt

This gives a straight line with a slope -k and intercept InC0

X/ Vd = C0 (x being the amount of drug given)

So, Vd = X/C0

(Graph page 55 on pharma 8)

Question 7

On the graph C= C0e-kt, what does the time constant equal?

What is e?

How do we find it?

Answer 7

T = 1/k

e= the time it takes for the plasma volume to fall by a factor of e, which is 37% of its value.

The gradient of the curve at time 0 will be e.

(Graph, page 55 of pharma 8)

Question 8

What is t1/2?

What equation do we get if we derive the relationship between the time constant and the half life?

What is IN2?

Answer 8

T1/2 = the time is takes for the plasma concentration of a drug to fall by a half.

T1/2 = T x IN2

IN2 = 0.693

Question 9

How long does it take for elimination to be very close to completion in terms of half lives and time constants?

Answer 9

Half lives = 5

Time constant = 3

Question 10

What is clearance?

Answer 10

The volume of plasma that is cleared of drug in a unit of time (ml/min)

Rate of elimination = clearance x plasma concentration

Question 11

What ranges are we aiming for when we are giving boluses of a drug?

Answer 11

In the therapeutic range, but below the toxic level

Question 12

What is steady state?

What equations do we use for steady state in a constant infusion?

Give an example with an infusion of 200mg/min and elimination of 100ml/min?

How long will it take to achieve steady state and what is the equation?

Answer 12

Steady state = Css

Css is when input = output

(Rate of elimination = plasma volume x clearance)

So if infusion rate = 200mg per min and elimination = 100ml per minute

Css x 100 = 200

Css = 2mg/ml

5 half lives or 3 time constants
C = Css(1-e-kt). e is the the power of -kt

Question 13

What compartments and relationships do we have in a two compartment model?

What does drug distribution depend on in these compartment?

Answer 13

Input (to compartment 1)
Compartment 1 = V1
Output from compartment 1 (K10)

Compartment 2 = V2
Input from compartment 1 to 2 e.g. distribution = K12
Output from compartment 2 to 1 e.g. re-distribution = K21

Depends on drug factors e.g. lipid solubility, pKa etc.
Body factors: vasculature, receptors, contents etc.

Question 14

In a two compartment model what is Vd?

What is clearance?

Answer 14

Vd = the sum of V1 and V2

Sum of terminal clearance Cl10 = (V1 x K10)

And inter-compartmental clearance (Cl12) = V2 x K21

Note: V1 x K12 = V2 x k21

Question 15

In a two compartment model, how do we calculate transfer from V1 to V2?

And V2 to V1?

Answer 15

C1 (plasma concentration at volume 1) x Cl12

C2 x Cl21

Question 16

What are the differences between a two compartment and one compartment model in terms of initial fall in plasma volume and terminal elimination?

Initial plasma concentration with multiple boluses?

What will effect the rate of plasma clearance once an infusion stops?

Answer 16

Initial drop in plasma concentration will be quicker, but terminal elimination will be longer.

With multiple boluses the initial drop after each will become longer as there will be less of a gradient between the two compartments as the second fills and the system reaches steady state.

Once infusion stops, central compartment drops, favouring redistribution (represented by hydraulic model). The time taken for plasma volume to drop is dependent on central clearance rate and inter departmental transfer rate.

Fast central elimination but slow transfer = fast drop
Slow elimination but fast transfer = slow drop

Question 17

What are the components of the three compartment model?

Answer 17

Look at diagram on page 60, pharma 8

Question 18

In a three compartment model, which intercompartmental clearance is the slowest?

Answer 18

Between V1 and V3

Question 19

What is the most common three compartment model for propofol and what does this use?

Answer 19

Marsh = weight only

Question 20

What is the volume of distribution at steady state in the marsh model?

Answer 20

300l (bigger than body, so only a model)

Question 21

In a three compartment model, what are the three different half lives?

Answer 21

Rapid initial elimination
Intermediate elimination and redistribution
Terminal elimination half life

Question 22

What is the relationship between three compartment opiate clearance and pKa?

Answer 22

All weak bases. Lower pKa = more unionised in blood = faster interdepartmental clearance

However there are differences in clearance of each in each compartment, meaning that clearnace can’t be calculated from modelling, but is purely observational.

Question 23

What would be the difference in clearance between an infusion of fentanyl and an infusion of propofol, in a three compartment model?

Answer 23

Both rapidly redistribute

But intercompartmental clearnace is much quicker for fentanyl, so plasma volumes will stay higher for longer than propofol e.g. slower fall than propofol.

Question 24

What is elimination?

Answer 24

Anything that reduces plasma volume, so can include metabolism, excretion, redistribution etc.

Question 25

Draw the one, two and three compartment models from page 1 do structural formula.

Answer 25

Done