This document discusses principles of pharmacokinetic (PK) and pharmacodynamic (PD) modeling. It notes that while all models are imperfect, some can still be useful. Simple models require fewer assumptions but more data, while complex models replace assumptions with data. The aim is the simplest useful model. Example models show how PK data can predict exposure from different doses and how PK-PD models integrate exposure over time with drug effects. Direct PK-PD models have effects directly linked to concentrations, while indirect models have time delays between exposure and response. Indirect models may allow less frequent dosing. The document stresses designing PK-PD studies based on all available knowledge to test hypotheses and obtain informative data on concentration-effect and time relationships

1. Principles and Modelling of
Pharmacokinetic and
Pharmacodynamic Relationships
Graham Trevitt (CSO, XenoGesis)

2. 2

3. • “All models are wrong, but some are useful”
• George Box (statistician)
• “Perfect is the enemy of the good”
• Voltaire
• Models are based on data and assumptions - if either are wrong then the model
will likely fail to be useful
• A simple model often has more assumption but needs less data
• Replacing assumptions with data can often be challenging/$$$
• A general aim is to have the simplest useful model with minimal data/cost
• “Useful” can change with time
• A model that is useful in the discovery phase may be inadequate for clinical development
3

4. Example of a useful model
• Useful models describe what we already know to allow us to predict what we
don’t
• e.g. I know the plasma exposure from a single 10mg/kg dose, what do I expect trough
concentrations to be from a 30mg/kg dose twice a day (BID)?
• We can use models to generate hypotheses that challenge the model
• 30mg/kg BID is predicted to give unbound exposure in excess of my in vitro EC90 – let’s see
if that translates to efficacy in our pharmacology model
4
10mg/kg Data Model Simulation
Predicted concentration
>EC90 from Day 3 @
30mg/kg

5. Conc
EffectPercent
TIME
Conc
Pharmacokinetics, Pharmacodynamics and
PK-PD
Pharmacodynamics (PD)
• What the drug does to the
body
• Effect versus concentration
5
Pharmacokinetics (PK)
• What the body does to the drug
• Concentration versus time
PK-PD
• Effect versus time
• Integrated relationship between plasma exposure versus time (PK) and effect versus
concentration (PD) for a given dose and route of administration
If PK-PD is well understood, then changing the PK side of the model allows
us to predict response (e.g. repeat dose or from mouse to human)
TIMEEffectPercent

6. Basic PK model – Single compartment IV
• Amount of drug (A1) dosed into a single
compartment of volume V
• Clearance (volume of compartment from
which drug is removed per unit time) = Cl
• Rate of elimination = Cl/V
• Units of 1/time
• Rate of change of amount of drug =
amount of drug * Cl/V
• Differential equation
• d(A1)/dt = -Cl/V*A1
• Concentration of drug, C = Amount of
drug/V
6

7. Modelling observed data
• 2 parameters describe the
model: Cl and V
• If we have observed data at a
range of time-points (CObs,
red circles) for a given initial
dose (A1) we can fit the data
to estimate Cl and V
• What values best fit the
observed data?
7

8. What if the data doesn’t fit?
• New data set isn’t a good fit
to a single compartment
model
• A more complex model is
needed
• Adding an additional
compartment with volume
V2 and clearance between
this compartment and the
central compartment (Cl2)
allows us to capture the
observed data
8

9. Adding an oral compartment
• Drug now starts in
dose compartment
(amount Aa) and is
absorbed at a rate Ka
into the central
compartment
• The rest of the model
is a two compartment
model we used
previously
9

10. Adding a PD Effect
• We can now add parameters that combine
observed effect (EObs) to plasma (C)
• Example shown relates effect (E) to plasma
concentration (C) using an Emax model
• E=Emax*C/(C+EC50)
• This is an example of a direct PK-PD
relationship
10

11. TIME
Conc
Direct
Direct PK-PD models
• Simplest PK-PD scenario
• At all time-points, concentration in plasma
is directly related to effect
• Diagnostic observations:
• Maximum effect at maximum concentration
(occurs at Tmax)
• A plot of effect versus concentration can be
described by (for example) Emax and EC50
• E=Conc*Emax/(Conc+EC50)
• Classical, sigmoidal response curve on semi-log
plot
• In the example shown, EC50 = 10nM and
maximum effect is at Tmax (1h)
11
Effect and concentration versus time
Effect versus concentration

12. Indirect PK-PD
• Time delay in response due to signalling pathways, cell-
cycle, protein re-synthesis etc. results in delay in effect
relative to concentration
• Example shown is same PK/dose as previous slide,
but PK-PD is indirect
• Diagnostic observations
• Maximum effect occurs later than plasma Cmax (9h v 1h in
the example shown)
• Effect versus concentration shows “hysteresis” - same effect
at two different concentrations (e.g. 50% at 79nM and
0.7nM)
• Time delay can be described empirically (e.g. through
an effect compartment) but can be more mechanistic
• e.g. tumour growth as a function of biomarker/pathway
inhibition
• More complex models = more data
12
Effect and concentration versus time
Effect versus concentration
TIME
Conc
Indirect
Conc
Indirect

13. Impact of indirect v direct PK-PD
• When PK-PD is indirect, the
duration of effect may be
significantly greater than the
duration of exposure
• Less frequent dosing may be
needed than for direct PK-PD
• Plots show same underlying PK and
EC50
• Direct PK-PD needs BID dosing for
>70% effect
• Indirect PK-PD achieves >80% from QD
dose
13
Direct PK-PD: BID Dose schedule
Indirect PD-PD: QD dose schedule
Modelling the single dose PK-PD would allow for
the optimal design of the repeat dose study

14. Interpretation and design of PK-PD studies
• PK-PD experiments should be designed
• Integrate all available knowledge (PK, in vitro pharmacology
and biology) and design studies to test a hypothesis
• Select dose levels and sample times to investigate
concentration-effect and time dependence
• Avoid simple dose-effect interpretation
• Exposure drives efficacy, dose is simply a means to achieve exposure
• Efficacy where the only dose was 100mg/kg doesn’t tell us much other
than 100mg/kg does something…
• Obtain exposure-time and effect-time data where possible
14
Integrate modelling and simulation into PK-PD design to maximise value of studies

15. Summary
• Models integrate knowledge of a drug and can help support decision
making throughout the drug discovery process
• A model doesn’t have to perfect to be useful (but it does need to be
useful)
• Refine models as the project progresses to make them more useful –
replace assumptions with data
• PK models should be combined with biological knowledge/hypotheses to
design PK-PD studies for maximal value
• A sound understanding of PK-PD (including the limitations of the PD
model itself) is fundamental to the prediction of human dose
• Want to know more? Look out for the DMDG PK-PD modelling course
(info@dmdg.org)
15

16. Questions?
Contact info@xenogesis.com for support
16