IN CONFIDENCE © 2001-2009
A New Platform for Combining the ‘Bottom-Up’ PBPK Paradigm and
POPPK Data Analysis
Senior Scientific Advisor, Head of M&S Honorary Lecturer, University of Sheffield
PKUK, 25-27 Nov 2009, UK
Masoud Jamei
IN CONFIDENCE © 2001-2009
Current: Geoff Tucker, Amin Rostami-Hodjegan, Mohsen Aarabi, Khalid Abduljalil, Malidi Ahamadi, Lisa Almond, Steve Andrews, Adrian Barnett, Zoe Barter, Kim Crewe, Helen Cubitt, Duncan Edwards, Kevin Feng, Cyrus Ghobadi, Matt Harwood, Phil Hayward, Masoud Jamei, Trevor Johnson, James Kay, Kristin Lacy, Susan Lundie, Steve Marciniak, Claire Millington, Himanshu Mishra, Chris Musther, Helen Musther, Sibylle Neuhoff, Sebastian Polak, Camilla Rosenbaum, Karen Rowland-Yeo, Farzaneh Salem, David Turner, Kris Wragg
Previous: Aurel Allabi, Mark Baker, Kohn Boussery, Hege Christensen, Gemma Dickinson, Eleanor Howgate, Jim Grannell, Shin-Ichi Inoue, Hisakazu Ohtani, Mahmut Ozdemir, Helen Perrett, Maciej Swat, Linh Van, Hua Wang, Jiansong Yang & .... Many others
Acknowledgement: The Team
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Grants Received by Simcyp
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Top-Down:Sparse Samples Analysis
Clinical Studies
Bottom-Up:Systems Biology/Pharmacology/Pharmacokinetics
Assessing vs Anticipating Covariate Effects
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Data-Driven (Top-Down) Approach
C=Cie-kit
Empirical
1
2Compartmental
(Ide
et
al.
2009)
Semi/Physiological
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Data-Driven (Top-Down) Approach
A primary objective of population pharmacokinetic (POPPK) studies is to estimate the inter-individual variability in PK parameters and identify the covariates that may account for the variability.
(JPP 2004)
If the goal is hypothesis testing, the practical implication is that one cannot fully discriminate between true and false between twohighly correlated covariates, other than for very strong covariates or large data sets.
The power of selecting a true covariate decreases with increasing correlation to any false covariate.
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Trends in Covariate Analyses in POPPK Studies
Contribution to new knowledge or confirmation of existing information?
Chetty and Rostami (PKUK 2008)
Aim: Assessing the relationship between the knowledge of human physiology and biology (system pharmacology) and the reported covariate in POPPK studies. A total of 140 papers from 5 journals were reviewed and they were classified as ‘Old’ (1990-1997) and ‘Recent’ (2006-2007) studies.
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graphs univariate posthoc 2 criteria prior knowledge
other
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No o
f Papers
The difference in the objective function was the most commonly used criterion for inclusion of a covariate in the final model of old studies. Multiple criteria including DOF, graphs, likelihood ratio and clinical relevance were used in recent studies.
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Trends in Covariate Analyses in POPPK Studies
• Covariates that were commonly included in the final model in both old and recent categories were demographic factors, hepatic and kidney function, drug dosing and interactions.
• Extensive information already exists on the impact of these factors on drug disposition.
• Covariate analyses may benefit from a priori identification of influential variables using virtual populations.
Chetty and Rostami (PKUK 2008)
Commonly Used Covariates
Sex
Age
Weight
BSA
BMI
Dose
Dosing regimen
Formulation
CLcr
Concurrent medication
Hepatic/Renal function
Plasma albumin
Smoking
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Bottom-Up: Systems Pharmacology Approach Using PBPK Modelling.
Bioavailability: release, dissolution, stability, permeability, efflux and/or uptake transport, gut wall and hepatic first pass metabolism, ...
Metabolism: unbound fraction, efflux and or uptake transport, enzyme abundace, blood flow, HSA, Heamatocrite, induction, inhibition, ...
Distribution: unbound fraction, blood flow, efflux and/or uptake transport, organ size, HSA, ... PBPK Models
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Mechanistic IVIVE & PBPK
SystemsData
Drug
DataTrial
Design
Population Pharmacokinetics &
Covariates of ADME
Combining Physiological and Drug-dependent Data
(Jamei et al., 2009)
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POPPK and Covariate Effects
CL = Typical parameter estimate x (Body weight/13) 3/4
x [1 - 0.0542 x (Cholesterol - 5.4)] x [1 - 0.00732 x (Haematocrit - 31)] x [1 + 0.000214 x (Serum creatinine - 524)]
The typical values refer to a patient with a body weight of 13 kg, cholesterol of 5.4 mmol l-1, serum creatinine of 524 mmol l-1 and a haematocrit of 31%.
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Age(Distribution in Population)
Ethnicity Disease
Sex(Distribution in Population)
Genotypes(Distribution in Population)
Height
Weight
Body Surface
Area
LiverVolume
Heart Volume
BrainVolume
LiverWeight
MPPGLHPGL
Enzyme &Transporter AbundanceIntrinsic
Clearance
Body Fat
CardiacOutput
CardiacIndex
SerumCreatinine
Renal Function
Plasma Proteins
&Haematocrit
The Complexity of Covariates
(Updated after Jamei et al., 2009)
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QH . fu/B:P.Uptake.CLuint
QH + fu/B:P.Uptake.CLuint
CLH =
Culiver/Ctotal (blood)>fu/B:P if drug is substrate for uptake transporters
Culiver/Ctotal (blood)<fu/B:P if drug is substrate for efflux transporters
fu/B:P . Uptake = Culiver/Ctotal (blood)
Liver Well-Stirred Model
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fu/B:P=fu
CB/CpMin (CB/Cp) = 1- Heamatocrit
Max (CB/Cp) = ∞
CB/Cp = (CRBC:CP)*HC + (1- HC)
Proportion of cardiac output 22% and 7% for portal vein and arterial liver blood supply, respectively)
Cardiac output based on BSA and age (2.5, 4, 3 and 2.4 L/min/m2 for 1, 10, 20 and
80 years of age, respectively)2
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Ca
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c I
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ex
(L/m
in/m
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Age: - ChildrenSex: - Female
Covariation of Hc:
Environment: - High AltitudeIndividual Attributes: - Athletes
Liver Blood Flow & fu/B:P
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Liv
er
Volu
me (
L)
Body Weight (kg)
LV = 0.722 x BSA1.176
LV = 1.38 x (BW/70kg)0.75
Fanta et al – “Developmental PK of ciclosporin: A population pharmacokinetic study in paediatric transplant patientsBr J Clin Pharmacol 64:772, 2007(with Corrections)
Top-Down vs Bottom-Up
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[1 - 0.00732 x 100*(HC - 0.31)]
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CL Multiplier (Top-Down)
CL Multiplier (Bottom-Up)
Heamatocrit
Rela
tive C
hange in C
L
fu/B:P.CLuintCLpo Clpo fu/[(CRBC/Cp)*HC + (1- HC)] fu = 0.037 and CRBC/Cp = 1.8fu/B:P = 0 0.0296 (at HC = 0.31)
[[0.037/[1.8*HC + (1- HC)] ]/ 0.0296]
Top-Down vs Bottom-Up
(Jamei et al., 2009)
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Tune design parameters to fit observations
Parameter Estimation Module
Simcyp simulation
Trial and Error
Tune design parameters to fit observations
Parameter Estimation (PE) Module
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Overall Settings
Parameter Estimation Module
Predicted Parameters
Parameter Estimation Module Overview
DVs Models Design Parameters
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PK Profiles Template
Route of administration can be oral or intravenous (bolus and/or infusion).
Dosing regimen can be single or multiple dosing and irregular dosing for different individuals is also supported.
The number of observation and their related sampling times for individuals can independently be entered.
The observations and dosing times can be entered in any order for any of subjects.
The subjects covariates (if any) are only needed once.
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Some of Available Models
Minimal and full PBPK models
VenousBlood
ArterialBlood
Lung
Adipose
Bone
Muscle
Skin
Spleen
Portal Vein
PO DoseIV Dose
Brain
Heart
Liver
Kidney
Gut
Small Intestine
Portal Vein
Liver SystemicCompartment
ka
QH
QPV QPV
QHA
Hepatic Clearance
PO
IV
Renal Clearance
Gut Metabolism
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EW: Extracellular Water
IW: Intracellular Water NP: Neutral Phospholipids
NL: Neutral Lipids AP: Acidic Phospholipids
KtP-off
P
PCapillary blood
EW
IW
pH=7.4
pH=7.4
pH=7
-ve
NP
NL
+ve
+ve
+ve
KtNP-on
KtNP-off
KtNL-on KtNL-off
KtEW-in
KtIW-in KtIW-out
KtEW-out
KP-off
KP-on
+ve
P
+ve KtP-on
KtP-off
KtAP-on KtAP-off
Ktel
AP
Some of Available Models
Tight junction
Bile
OATP1B1 OATP1B3 OCT1
P-gp
MRP3
BCRP
MRP2
Sinusoidal membrane
Canalicularmembrane
Permeability-limited Liver Model - Hepatobiliary Transporters
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Some of Available Models
One-compartment absorption, Compartmental Absorption and Transit, and Advanced Dissolution, Absorption and Metabolism (ADAM) models.
Stomach
Metabolism
Portal Vein Liver
PBPK Distribution Model
Enterocytes
Faeces1 2 3 4 5 6 7
Small Intestine Lumen
Jejunum I & IIDuodenum Ileum I Ileum II Ileum III Ileum IV
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Enterohepatic Recirculation (EHR) including gallbladder emptying
Figure from Roberts et al. 2002
Some of Available Models
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Some of Available Models
Up to 4 compounds and two of their metabolites in addition to their auto and mutual interactions (inhibition/induction).
Enterocytes
Portal Vein
LiverSystemic
Compartment
Qvilli
QH
QPV QPV
QHA
Hepatic Metabolismof metabolite
Renal Clearanceof metabolite
Gut Metabolismof metabolite
Ve
no
us B
loo
d
Art
eri
al
Blo
od
Lung
Adipose
Bone
Brain
Heart
Kidney
Muscle
Skin
Liver
Spleen
Gut
Portal Vein
PO
IV
Hepatic Metabolism
Gut Metabolism
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Design Parameters
Virtually any parameter can be selected.
It can be population-dependent parameters or drug-dependent parameters.
Up to 10 parameters can simultaneously be fitted.
The initial values and ranges are provisionally assigned but can be changed by users.
Currently, uniform, normal and log-normal distribution of parameters are included.
Covariates are inherently included!
IN CONFIDENCE © 2001-2009
Direct/random search methods (Hooke-Jeeves, Nelder-
Mead, …);
Genetic Algorithms (GA);
Combined Algorithms:
Begin with a global optimisation method (GA) and
then switch to a local optimisation method; e.g., HJ or
NM.
Optimisation Algorithms
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Optimisation Algorithms - Nelder-Mead (Simplex)
Nelder-Mead (1965) method which is also called downhill simplexis a commonly used nonlinear optimisation algorithm.
Nelder-Mead includes the following steps:
• Reflection;• Expansion;• Contraction;• Reduction;
http://optlab-server.sce.carleton.ca/POAnimations2007/NonLinear7.html
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Design Parameter, e.g. CL
Ob
ject
ive
Fu
nct
ion
Va
lue
(OF
V)
Local minima
Global minimum
Local vs Global Minimum
Initial value
Another Initial value
IN CONFIDENCE © 2001-2009
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Log O
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Log O
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Objective Function Landscapes
ni
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ii )t,(fy
ni
1i2
i
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ii
y
)t,(fy
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Genetic Algorithms (GAs)
Stochastic search and optimisation technique
Search in a ‘collection’ of potential solutions
Work with a representation of the design parameters
Guided by objective function, not derivatives
Uses probabilistic transition rules
Holland (1975) ; Goldberg (1983, 1989)
GAs are based on Darwin's theory of evolution and mimic biological evolution (Survival of the Fittest).
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GAs Stages
Assessing candidate solutions according to the defined objective function and assign fitness based on the ability or utility of the candidate solutions.
Selecting candidate solutions based on a probabilistic function of their fitness.
n
i
iFitness1
ii
FitnessyProbabilit Production-Re
After adjusting fitness values, candidates are selected for mating.
Then genetic operations, e.g. cross-over and mutation are applied.
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Genetic Algorithms Stages
Randomly Assigned Candidates
Evaluate Candidates
Rank Candidates
Reproduce New Candidates
Recombination and Mutation
Select a New Set of Candidates
Set of Candidate Parameters
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Maximum Likelihood (ML) Approach
Maximising the probability of obtaining a particular set of data, given a chosen probability distribution model. This can be done by maximising the so called log-likelihood function:
N
iiiiii
dpYpL1
2 )),|(),|(log()(
The optimal ML estimate can be found from:
2
2
21
( ( , )) 1( ) ln
2
kMk ki i
ML i
k
y f XO
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Maximum a Posterior (MAP) Approach
MAP estimation is a Bayesian approach in the sense that it can exploit additional information on the supplied experimental data.
P
j
2
j2
j
2
jjN
1i
2b
i102b
i10
2
iiMAP )ln(
)())t,(fbb(ln
))t,(fbb(
))t,(fy()(O 2
2
Consequently if the user has prior knowledge regarding the parameters then the MAP should in theory provide more accurate estimations of the design parameters than the Maximum Likelihood which only requires experimental measurements.
Where β={b0, b1, b2} vector defines the variance model:
Additive β={b0, 0, 1} Proportional β={0, b1, 1} Combined β={b0, b1, 1}
MAP differs from ML in that it uses prior distribution of parameters p(θ):
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Expectation-Maximisation (EM) Algorithm
E-step:
Determining the conditional expectation using Monte Carlo (MC) sampling and updating MC pool for each individual after each iteration.
M-step:
Maximise this expectation with respect to θ and updating population parameters and variance model parameters.
In order to determine the ML or MAP estimations we need to use an optimisation algorithm.
The Expectation-Maximisation (EM) algorithm is one of the most popular algorithms for the iterative calculation of the likelihood estimates.
The EM algorithm was first introduced by Dempster et al (Dempster, Laird et al. 1977) and was applied to a variety of incomplete-data problems and has two steps which are the E-step and the M-step.
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There are six sheets: PE Input Sheet, Summary, Individual and Pop fit, Observed Vs Predicted, Residual Errors and Parameters Trend (Ind).
PE Reports
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Slide adapted with permission from Malcolm Rowland
An ideal modelling platform would be one that could incorporate strengths of population analysis (top-down) and PBPK (bottom-up) ; ... Middle-out!
Future Vision
Adoption of middle out approach; break the preclinical/clinical PK model divide.
Bring PBPK models into all phases of clinical drug development. Now increasingly possible with the availability of commercially supported software.
Complete learning by Phase II. Refine preclinical PK parameters with early experimental human/patient (Phase 0, I & II) data.
Phase III: Confirming phase. Increasingly ask whether observed concentration-time data are within expectations, instead of ‘hunting’ for PK covariates and relationships.
Look for similar developments emerging in PD.
Move to a better model-based drug development paradigm.