This is a brief presentation on PK-PD modeling.

1. Introduction to
PK-PD Modeling
Seminar by,
Pooja SG
Final Year PG Resident
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2. Outline of the Seminar
• Definitions
• Pharmacokinetic modeling
• Pharmacodynamic modeling
• Population PK-PD modeling
• Software for PK-PD modeling
• Role of PK-PD modeling in drug development
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3. Pharmacokinetics
• Describes the concentration-time course of the drug in the
body after administration of a certain dose of the drug.
• What the body does to the drug - ADME
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4. Pharmacodynamics
• Describes the intensity of drug effect in relation to the
concentration
• What the drug does to the body
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5. Modeling
• Description of a biological process by which one can
predict one variable from another by using mathematical
and statistical principles
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6. What is PK-PD modeling?
• PK PD modeling combines both these (PK, PD) approaches
and tries to establish models in order to describe effect – time
course directly.
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7. What is PK PD modeling?
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8. Rationale for PK-PD modeling
Administered dose of the drug
Resulting concentration in the
measurable compartment of body
Intensity of the effects caused by
the attained concentrations
PK & PD determine the relationship between:
Rational
use of
drugs and
design of
regimens
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9. Rationale for PK-PD modeling
Examples
• From single dosing to multiple
dosing regimen
• From intravenous to oral route
Extrapolation of data
(PK/PD data)
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10. Components of PK PD modeling
PK Model
PD Model
Integration of PK and PD
model
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11. Pharmacokinetic
modeling
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12. PK Parameters
Primary Parameters
Clearance (CL) and Volume of distribution (Vd)
Secondary Parameter
Half life (t1/2)
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13. Broad Categories of PK Models
1. Compartmental models
2. Non compartmental models
3. Physiologically based PK models (PB PK models)
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14. Compartmental models
Most frequently preferred:
✓Provide continuous conc. - time profile in the body that can
be related to continuous effect – time profile
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15. Assumptions for compartmental concept
• Human body is made of compartments.
These compartments are not anatomical, physiological but
hypothetical.
• Each compartment is well stirred instantaneously so that
drug is distributed uniformly throughout the compartment.
• Elimination occurs only from central compartment.
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16. One compartmental Model
Compartment
Drug
Dose
Elimination
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17. One compartmental Model
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18. Cp vs Time
Log Cp vs Time
Cp: Plasma Concentration
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19. Two Compartmental Model
Central
Peripheral
Drug
Dose
Elimination
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20. Two Compartmental Model
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21. Cp vs Time
Log Cp vs Time
Cp: Plasma Concentration
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22. Allotment of compartments
• Central compartment – blood, extracellular space, well
perfused organs like liver, kidney, heart, lungs
• Peripheral compartment – poorly perfused organs like fat,
bones, skin
• Brain
➢ Lipophilic drugs – central
➢ Hydrophilic drugs – peripheral
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23. Non Compartmental Models
• Also known as model-independent
• Do not rely on any assumptions
When to go for it?
• When the distinction between one, two or multi
compartment model is not clear
• Insufficient no. of samples from each subject so that
characterization of model becomes difficult e.g. neonates,
animals (as no. of samples will be less due to concerns of
blood loss)
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24. Non Compartmental Models
• PK parameters are derived from AUC
Reason:
• Of all the PK parameters, AUC is most insensitive for
change in compartment models.
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25. Non Compartmental Models
Parameters calculated
• AUMC (area under the first moment curve)
Area under concentration times time versus time curve
• MRT (mean residence time) = AUMC/AUC
• Kel = 1/MRT
• Clearance (CL) = Dose / AUC
• Vol. of dist. in steady state (Vss) = CL x MRT
= (Dose x MRT)/AUC
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26. Physiology Based PK modeling
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Jones H, Rowland-Yeo K. Basic concepts in physiologically based pharmacokinetic
modeling in drug discovery and development. CPT Pharmacometrics Syst Pharmacol.
2013 Aug 14;2:e63

27. Pharmacodynamic
modeling
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28. Factors to be considered while selecting a PD
model
• Drug used
• Nature of the response
• Degree of linearity in the effect concentration curve
• Potential for achieving maximal effect
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29. Broad Categories of PD Models
PD models for steady state
conditions
1. Fixed effect model or
quantal effect model
2. Linear model
3. Log linear model
4. Emax model
5. Sigmoid Emax model
PD models for non steady
state conditions
1. Direct vs Indirect link
models
2. Direct vs Indirect
response models
3. Soft vs hard link models
4. Time invariant vs time
variant models
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30. PD models for
steady state conditions
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Meibohm B, Derendorf H. Basic concepts of pharmacokinetic/pharmacodynamic
(PK/PD) modeling. Int J Clin Pharmacol Ther. 1997 Oct;35(10):401-13.

31. Fixed Effect (quantal effect) Model
• It relates drug concentration with the statistical likelihood
of a predefined, fixed effect to be present or absent
• Eg: Ototoxicity occurs when gentamicin therapy exceeds
the levels of 4 μg/mL
E=ototoxicity when C > Cthreshold(4 μg/mL)
• Given the variability in the population, the threshold conc
varies among individuals
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32. Fixed Effect Model
• Then, this model can predict
• If the conc is > 4 μg/mL, 50% probability to observe ototoxicity
• If the conc is > 7 μg/mL, 90% probability to observe ototoxicity
• This model can only be used as approximation of dose-
response relationships
• They may not be useful for prediction of complete effect-
time profiles
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33. Linear Effect Model
• Model assumes that conc. is
directly proportional to drug effect
e.g. Salivary flow rate and plasma
concentration of pilocarpine infusion
• Most intuitive model
• Generally used for IV infusions
Mathematical Expression of Model
E = m x C + E0
(E0: Baseline effect, m:proportionality factor
(slope), C: Concentration of drug)
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m

34. Log-linear Model
• Applicable when the conc-
effect curve is hyperbolic
• Log conc-effect relationship is
roughly linear in the range of
20 to 80%
Mathematical Expression of
Model
E = m * log C + b
(m and b are the slope and intercept in a
plot of Effect E vs Log C)
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35. Emax Model
• Falls in line with the receptor theory
• Takes into account the intrinsic activity and potency of drug
(Emax: Maximim effect possible, E50: Concentration causing 50% effect)
(Emax refers to intrinsic activity of drug, E50 to its potency)
• This model can describe complex concentration effect
relationships
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Mathematical Expression of Model Receptor occupancy theory

36. Emax Model
Concentration-effect relationship from Emax model
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37. Sigmoidal Emax model
• Extension of the Emax model
• It describes for many drugs that appear to be S shaped rather
than hyperbolic as described by more simple Emax model.
• Excellent model for combining data across doses
• Allows accurate estimation of differences between doses
Mathematical Expression of Model
(n is the slope factor, that determines the shape of the curve, larger the n, steeper is the
linear phase of Log-conc-effect curve)
n is an exponent describing the number of drug molecules that combine
with each receptor molecule.
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38. Sigmoidal Emax model
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39. PD models for
non steady state conditions
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40. Direct versus Indirect Link Models
• Also known as Biophase distribution model
• To model the time lag between the plasma concentration in
the central compartment and response.
[D] plasma = [D] at site
• This could be due to multiple mechanisms: delayed
distribution to organs, active metabolite formation etc
• Direct Link: When there is no lag
• Indirect link: When there is time lag
• An additional effect compartment is built into the model to
minimize the time-lag between the concentration and effect
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41. Indirect Link
Direct Link
This model has been used to characterize Pk-PD of several drugs
whose concentrations could not be corelated with effect.
Eg: midazolam, pancuronium, alprazolam
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42. Direct versus Indirect Response Models
• Used when there is a lag time for development of a
response even after drug reaches the target site
• Direct response – Observed effect of the drug is directly
mediated by its interaction with response structures
(receptors / targets)
• Indirect response – mechanism of action of drug
mediated through other pathways like gene expression
• Mechanism: time required for inhibition or stimulation of
synthesis, processes etc.
eg: effect of glucocorticoids, warfarin
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43. Direct versus Indirect Response Models
Indirect response model for the effect of fluticasone propionate on the
number of lymphocytes in blood
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44. Soft versus Hard Link
Soft Link
• Both PK and PD data are
used to determine link
Hard Link
• PK data with additional
information from in vitro
studies are used
• PD is not used
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45. Time Variant versus Invariant
The previously discussed PK/PD models all assume that
• Only the measured concentration and observed effects
undergo time dependent changes
• But the involved PD parameters e.g Emax and E50 are
constant over time.
• Thus, these models are time invariant
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46. Time-variant Models
Counter/Anti clock-wise hysteresis in effect versus conc
loop:
• Same drug concentration produces two different
magnitudes of pharmacological effects measured effect
increases with time (Sensitization)
• Small effect at a given drug concentration; however, after
some time has passed the same drug concentration gives
rise to a greater measured effect than expected
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47. Time-Variant Models
Counter/Anti clock-wise hysteresis:
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• Mechanisms: delayed
uptake into active site,
active metabolites,
upregulation etc
• Eg: Fall in standing SBP
by ISDN is greater at
declining phase

48. Time-variant Models
Clock-wise hysteresis loop in effect vs conc:
• Same drug concentration produces two different
magnitudes of pharmacological effects measured effect
decreases with time (Tolerance)
• Greater effect at a given drug concentration; however, after
some time has passed the same drug concentration gives
rise to a smaller measured effect than expected
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49. Time-variant Models
Clock-wise hysteresis:
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• Mechanisms: active
antagonistic metabolites,
receptor down regulation,
negative feedback etc
• Eg: natriuretic response of
furosemide, opioids

50. Population PK-PD modeling
The non-linear mixed-effects modeling software (NONMEM) introduced
by Sheiner and Beal is one of the most commonly used programs for
population analysis. 20-02-2020 50
Purpose: Characterization of interindividual variations
in PK/PD parameters
This includes the search for covariates which contribute
to interindividual variability, affecting PK/PD
relationship.
Eg: weight, age, renal function & disease status
The detection and quantification of covariate effects,
their influence on the dosage regimen design.

51. Software for PK-PD modeling
• WinNonLin
• GastroPlusR
• P-Pharm
• PH/EDSIM
• MEDICI – PK
• Pmetrics
• NONMEM
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52. Role of PK-PD modeling in Drug Development
• Allows successful extrapolation of preclinical results to
predict effective and toxic drug concentrations
• Helps in selection of appropriate doses for subsequent
phases
• Helps to study inter-individual differences
• Helps in dose adjustments in special populations
• Makes drug development more rational and efficient
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53. Case study
PK/PD Analysis to Identify Reason for Study Failure
• An example of Direct Link/Response Model
KG Kowalski, S Olson, AE Remmers and MM Hutmacher, Modeling and Simulation
to Support Dose Selection and Clinical Development of SC-75416, a Selective Cox-2
Inhibitor for the Treatment of Acute and Chronic Pain, Clinical Pharmacology &
Therapeutics, Vol83, 857-866, 2008
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54. Background
• A selective COX-2 Inhibitor- SC-75416
• Preclinical and PK from Healthy volunteers suggested 60
mg SC-75416 would provide pain relief (PR) similar to 50
mg rofecoxib (Vioxx)
• In a dose-ranging study for pain relief in post-surgical
dental patients:
• Single oral dose of placebo, 3, 10, and 60 mg SC-75416
CAPSULES were compared with 50 mg rofecoxib
• 10 and 60 mg doses were better than placebo, but did not achieve
PR comparable to 50 mg rofecoxib
• Drop out rate was higher in SC-75416 groups than rofecoxib
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55. Phase I (Healthy Volunteer study)
2 Individual (gray lines) and median (K) SC-75416 plasma concentrations–time
profiles over 6 h following a single 60 mg oral dose of SC-75416 administered as
an oral solution in healthy volunteers (N ¼ 30) and in capsule form in post-
surgical dental patients (N ¼ 50).
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56. • A PK/PD model was developed to predict how a 60 mg
oral solution dose may have performed in the post-oral
surgery pain study
• These models predicted that a dosage form with a PK
profile similar to the 60 mg oral solution would have had
Pain response comparable to 50 mg rofecoxib.
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57. • Moreover, extrapolations suggested that higher doses could
achieve clinically superior pain response relative to 50 mg
rofecoxib or other non-steroidal anti-inflammatory drugs
(NSAIDs).
• This hypothesis encouraged the team to consider an acute
pain development strategy, with the high dose providing
efficacy differentiation from the other products.
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58. • Results from a Subsequent Clinical Study Comparing Oral
Solution SC-75416 and Ibuprofen 400 mg
Rafecoxib was withdrawn by the time they conducted the next study
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Modeling results used to
• Identify reason for trial failure
• Predict outcome for new formulation
• Facilitate dose selection

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In another example,
In an oncology development program,
• The relationships between pharmacokinetic and safety/efficacy
were investigated in a phase I study conducted in patients.
• PK-PD model was developed and analyzed for various dose-range
• These results helped to skip phase II and were used to design the
pivotal phase III study
• Saved 12-18 months of development time
Reigner BG, Williams PE, Patel IH, Steimer JL, Peck C, van Brummelen P. An
evaluation of the integration of pharmacokinetic and pharmacodynamic principles
in clinical drug development. Experience within Hoffmann La Roche. Clin
Pharmacokinet. 1997 Aug;33(2):142-52.

61. Thank you ☺
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