a new platform for combining the ‘bottom-up’ pbpk paradigm and poppk data analysis

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

[email protected]

Masoud Jamei


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


Top-Down:Sparse Samples Analysis

Clinical Studies

Bottom-Up:Systems Biology/Pharmacology/Pharmacokinetics

Assessing vs Anticipating Covariate Effects


Data-Driven (Top-Down) Approach

C=Cie-kit

Empirical

1

2Compartmental

(Ide

et

al.

2009)

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)

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.


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.

0

20

40

60

not described

graphs univariate posthoc 2 criteria prior knowledge

other

old recent

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.


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


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


Mechanistic IVIVE & PBPK

SystemsData

Drug

DataTrial

Design

Population Pharmacokinetics &

Covariates of ADME

Combining Physiological and Drug-dependent Data

(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%.


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)


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


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

2.5

3

3.5

4

4.5

0 20 40 60 80 100Age (years)

Ca

rdia

c I

nd

ex

(L/m

in/m

2)

Age: - ChildrenSex: - Female

Covariation of Hc:

Environment: - High AltitudeIndividual Attributes: - Athletes

Liver Blood Flow & fu/B:P


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0.9

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1.5

10 20 30 40 50 60 70

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


[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)


Tune design parameters to fit observations

Parameter Estimation Module

Simcyp simulation

Trial and Error

Tune design parameters to fit observations

Parameter Estimation (PE) Module


Overall Settings

Parameter Estimation Module

Predicted Parameters

Parameter Estimation Module Overview

DVs Models Design 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

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


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


Tight junction

Bile

OATP1B1 OATP1B3 OCT1

P-gp

MRP3

BCRP

MRP2

Sinusoidal membrane

Canalicularmembrane

Permeability-limited Liver Model - Hepatobiliary Transporters



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


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).

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


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!


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


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


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


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45

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-4

-2

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2

4

Vss (L)

Log O

FV

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23

45

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Vss (L)

Log O

FV

Objective Function Landscapes

ni

1i

2

ii )t,(fy

ni

1i2

i

2

ii

y

)t,(fy


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).


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.


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


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


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):


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.


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

PE Reports


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.

a new platform for combining the ‘bottom-up’ pbpk paradigm and poppk data analysis

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