8. Modelling and 2/3 compartment model Flashcards
Why do we use pharmacokinetic modelling?
To predict the behaviour of a drug e.g. change in plasma concentration with time. Need to take ADME into account.
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?
Elimination which is either post-metabolism or unchanged drug.
It is proportional to the plasma concentration and this is called a first order relationship.
If a curve is hyperbolic and slopes down with time, what is this called?
When would we see this?
A negative exponential. Y = e (to the power of -x)
When the level of something is reducing e.g. plasma concentration of a drug
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?
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)
What are the important elements that need to be considered in a one compartment elimination model?
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
To find the constant of a given drug’s elimination, what do we do?
What kind of graph does this give?
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)
On the graph C= C0e-kt, what does the time constant equal?
What is e?
How do we find it?
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)
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?
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
How long does it take for elimination to be very close to completion in terms of half lives and time constants?
Half lives = 5
Time constant = 3
What is clearance?
The volume of plasma that is cleared of drug in a unit of time (ml/min)
Rate of elimination = clearance x plasma concentration
What ranges are we aiming for when we are giving boluses of a drug?
In the therapeutic range, but below the toxic level
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?
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
What compartments and relationships do we have in a two compartment model?
What does drug distribution depend on in these compartment?
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.
In a two compartment model what is Vd?
What is clearance?
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
In a two compartment model, how do we calculate transfer from V1 to V2?
And V2 to V1?
C1 (plasma concentration at volume 1) x Cl12
C2 x Cl21
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?
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
What are the components of the three compartment model?
Look at diagram on page 60, pharma 8
In a three compartment model, which intercompartmental clearance is the slowest?
Between V1 and V3
What is the most common three compartment model for propofol and what does this use?
Marsh = weight only
What is the volume of distribution at steady state in the marsh model?
300l (bigger than body, so only a model)
In a three compartment model, what are the three different half lives?
Rapid initial elimination
Intermediate elimination and redistribution
Terminal elimination half life
What is the relationship between three compartment opiate clearance and pKa?
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.
What would be the difference in clearance between an infusion of fentanyl and an infusion of propofol, in a three compartment model?
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.
What is elimination?
Anything that reduces plasma volume, so can include metabolism, excretion, redistribution etc.
Draw the one, two and three compartment models from page 1 do structural formula.
Done
