A New Platform for Combining the ‘Bottom-Up’ PBPK Paradigm and POPPK Data Analysis

A New Platform for Combining the
‘Bottom-Up’ PBPK Paradigm and
POPPK Data Analysis

Masoud Jamei
Senior Scientific Advisor, Head of M&S
Honorary Lecturer, University of Sheffield

M.Jamei@Simcyp.com

PKUK, 25-27 Nov 2009, UK

IN CONFIDENCE © 2001-2009

Acknowledgement: The Team

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


Grants Received by Simcyp


Assessing vs Anticipating Covariate Effects

Top-Down:
Sparse Samples Analysis
Clinical Studies

Bottom-Up:
Systems Biology/Pharmacology/Pharmacokinetics


Data-Driven (Top-Down) Approach
(Ide et al. 2009)

1
C=Cie-kit

2
Empirical Compartmental Semi/Physiological

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)

The power of selecting a true covariate decreases with increasing
correlation to any false covariate.

If the goal is hypothesis testing, the practical implication is that one
cannot fully discriminate between true and false between two
highly correlated covariates, other than for very strong covariates or
large data sets.


Trends in Covariate Analyses in POPPK Studies

Contribution to new knowledge or confirmation of existing
information?
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.

60 old recent
No of Papers

40

20

0
not graphs univariate posthoc 2 criteria prior other
described knowledge

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.

Chetty and Rostami (PKUK 2008)

Trends in Covariate Analyses in POPPK Studies

Commonly Used Covariates
• Covariates that were commonly Sex
included in the final model in both
old and recent categories were Age
demographic factors, hepatic and Weight
kidney function, drug dosing and BSA
interactions. BMI
• Extensive information already Dose
exists on the impact of these
Dosing regimen
factors on drug disposition.
Formulation
• Covariate analyses may benefit
from a priori identification of CLcr
influential variables using virtual Concurrent medication
populations. Hepatic/Renal function
Plasma albumin
Smoking
Chetty and Rostami (PKUK 2008)

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


Combining Physiological and Drug-dependent Data

Drug
Data
Systems Trial
Data Design

Mechanistic
IVIVE & PBPK

Population Pharmacokinetics
&
Covariates of ADME
(Jamei et al., 2009)

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%.


The Complexity of Covariates
Genotypes
(Distribution in Population) Renal
Function
Plasma Body Ethnicity Disease
Proteins Fat Serum
& Creatinine
Haematocrit

Sex Age
(Distribution in Population) (Distribution in Population)

Height Brain
Body Volume
Heart Surface
Volume Area
Weight
MPPGL
HPGL
Cardiac Cardiac
Liver Output Index Enzyme &
Volume Transporter
Liver Intrinsic Abundance
(Updated after Jamei et al., 2009) Weight Clearance

Liver Well-Stirred Model

QH . fu/B:P.Uptake.CLuint
CLH =
QH + fu/B:P.Uptake.CLuint

fu/B:P . Uptake = Culiver/Ctotal (blood)

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


Liver Blood Flow & fu/B:P

4.5
Proportion of cardiac output

Cardiac Index
4
22% and 7% for portal vein and arterial liver

(L/min/m2)
blood supply, respectively) 3.5
3
Cardiac output based on BSA and 2.5
age (2.5, 4, 3 and 2.4 L/min/m2 for 1, 10, 20 and 2
80 years of age, respectively)
0 20 40 60 80 100
Age (years)

CB/Cp = (CRBC:CP)*HC + (1- HC)
fu
fu/B:P= Min (CB/Cp) = 1- Heamatocrit
CB/Cp
Max (CB/Cp) = ∞
Covariation of Hc:
Age: - Children
Sex: - Female

Individual Attributes: - Athletes Environment: - High Altitude


Top-Down vs Bottom-Up

1.5
LV = 0.722 x BSA1.176

LV = 1.38 x (BW/70kg)0.75
1.2
Liver Volume (L)

0.9

0.6
Fanta et al – “Developmental PK of ciclosporin: A
population pharmacokinetic study in paediatric
0.3 transplant patients
Br J Clin Pharmacol 64:772, 2007
(with Corrections)

0
10 20 30 40 50 60 70

Body Weight (kg)


Top-Down vs Bottom-Up

[1 - 0.00732 x 100*(HC - 0.31)]
Clpo  fu/[(CRBC/Cp)*HC + (1- HC)]
CLpo  fu/B:P.CLuint fu = 0.037 and CRBC/Cp = 1.8
fu/B:P = 0 0.0296 (at HC = 0.31)
[[0.037/[1.8*HC + (1- HC)] ]/ 0.0296]
1.4

1.2
Relative Change in CL

1

0.8

0.6
CL Multiplier (Top-Down)
0.4
CL Multiplier (Bottom-Up)
0.2

0
0 0.1 0.2 0.3 0.4 0.5 0.6
Heamatocrit
(Jamei et al., 2009)

Parameter Estimation Module

Tune design parameters
to fit observations
Simcyp simulation

Trial and Error

Parameter Estimation (PE) Module


Overall Settings
Parameter Estimation Module Overview

DVs Models Design
Parameters

Parameter Estimation Module

Predicted
Parameters


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.


Some of Available Models

Minimal and full PBPK models

Lung

PO Small Intestine Gut
Metabolism Adipose
ka
Bone

Portal Vein Brain

Heart
QPV QPV Venous Arterial
Kidney Blood
Blood
QHA Muscle

QH Skin
Liver Systemic
IV
Compartment
Liver
Hepatic Clearance
Renal Spleen
Clearance Portal Vein
Gut
IV Dose PO Dose



Permeability-limited Liver Model - Hepatobiliary Transporters

Capillary blood KP-on
KtP-off
P +ve
P KP-off pH=7.4
KtEW-in KtEW-out
KtP-off pH=7.4
+ve
P
KtP-on +ve
EW
Sinusoidal OATP1B1 OATP1B3 MRP3
KtIW-in KtIW-outOCT1
membrane
Tight junction
KtNP-on
P-gp
+ve

KtNP-off KtAP-on KtAP-off
NP MRP2
KtNL-on KtNL-off Bile
Ktel
+ve
BCRP
AP
-ve
NL pH=7
IW
EW: Extracellular Water NL: Neutral Lipids AP: Acidic Phospholipids Canalicular
membrane
IW: Intracellular Water NP: Neutral Phospholipids


One-compartment absorption, Compartmental Absorption and Transit,
and Advanced Dissolution, Absorption and Metabolism (ADAM) models.

Small Intestine Lumen

Stomach Duodenum Jejunum I & II Ileum I Ileum II Ileum III Ileum IV

1 2 3 4 5 6 7 Faeces

Enterocytes
Metabolism

PBPK Distribution
Model
Portal Vein Liver


Enterohepatic Recirculation (EHR) including gallbladder emptying

Figure from Roberts et al. 2002


Up to 4 compounds and two of their metabolites in addition to their auto
and mutual interactions (inhibition/induction).
Lung

Adipose

Bone Enterocytes Gut Metabolism
of metabolite
Qvilli
Brain
Venous Blood

Portal Vein
Heart Arterial Blood

Kidney
QPV QPV
Muscle QHA
Skin QH Systemic
Liver
Compartment
Liver
Spleen Hepatic Metabolism Renal Clearance
Portal of metabolite of metabolite
Vein Gut
IV Gut Metabolism
PO

Hepatic Metabolism


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!


Optimisation Algorithms

 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 - Nelder-Mead (Simplex)

Nelder-Mead (1965) method which is also called downhill simplex
is 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


Local vs Global Minimum
Objective Function Value (OFV)

Initial value
Another
Initial value

Local minima

Design Parameter, e.g. CL
Global minimum

28 IN CONFIDENCE © 2001-2009

Objective Function Landscapes

4

2 20
Log OFV

0
15

Log OFV
-2
10
-4 0
0 5
-6 1
0 1 0
1 2 0 2
2 1
3 3 2 3
Vss (L) 4 3
5 4 Vss (L) 4
5 4

i n in
yi  f (, t i ) 2

 y i  f (, t i ) 
2

i 1 yi2
i 1


Genetic Algorithms (GAs)

GAs are based on Darwin's theory of evolution and
mimic biological evolution (Survival of the Fittest).

 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 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.
Fitnessi
Re - Production Probabilit y i  n

 Fitness
i 1
i

 After adjusting fitness values, candidates are selected for
mating.

 Then genetic operations, e.g. cross-over and mutation are
applied.


Genetic Algorithms Stages
Evaluate Candidates

Randomly Assigned Set of Candidate
Candidates Parameters

Select a New Set of
Rank Candidates
Candidates

Recombination and Reproduce New
Mutation Candidates


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 
L()   log(  pi (Yi |  i ,  2 ) p( i |  , )d i )
i 1

The optimal ML estimate can be found from:

 ( yk  f ( X ki , ik )) 2 1 2 
 
M
OML (i )     ln  
k 1   2
2 


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.

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.

MAP differs from ML in that it uses prior distribution of parameters p(θ):

 ( yi  f (, t i )) 2  P  ( j   j ) 2 
 
N
O MAP ()     ln (b 0  b1f (, t i ) b 2 ) 2     ln( j )
2

i 1  ( b 0  b1f (, t i ) )  j  j
b2 2 2
 


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}


Expectation-Maximisation (EM) Algorithm

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.
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.


PE Reports

There are six sheets: PE Input Sheet, Summary, Individual and Pop fit, Observed
Vs Predicted, Residual Errors and Parameters Trend (Ind).


Future Vision

An ideal modelling platform would be one that could incorporate strengths
of population analysis (top-down) and PBPK (bottom-up) ; ... Middle-out!
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.
Slide adapted with permission from Malcolm Rowland

A New Platform for Combining the ‘Bottom-Up’ PBPK Paradigm and POPPK Data Analysis

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