Prof. Wilhelm Huisinga Computational Physiology Group
Universität Potsdam
Grundlagen und Anwendungen der Physiologie-basierten Toxikokinetik-Modellierung
47. Sitzung der HBM Komission 24./25. März 2014, Berlin
Prof. Wilhelm Huisinga 2
Outline 1. The potential 2. The structure of physiologically-based
toxicokinetic models 3. Parameterization (incl. underlying model
assumptions) and parameter sources 4. Example 5. Summary & References
Prof. Wilhelm Huisinga 3
• Model organisms • mouse as a model for human • yeast as a simple eukaryote
• Biological model: — interaction network — cartoon
• Mathematical model: — representation of biological model
in terms of mathematical language — in our context deterministic
differential or algebraic equations
The use of the term model in different contexts
orgptorg
inorgorgorg CPC
CQCdtdV ⋅−⎟⎟
⎠
⎞⎜⎜⎝
⎛−⋅= CL:
Prof. Wilhelm Huisinga 4
The potential
external exposure
systemic exposure (parent + metabolite)
exposure at site of action
effect
PBTK
MBTD PBTK modeling offers a way to • integrate data from various
sources • study ‘what-if’ scenarios • quantify the impact of
variability and uncertainty • identify critical parameters • ...
(PBTK= physiologically-based toxicokinetics, MBTD = mechanism-based toxicodynamics)
Prof. Wilhelm Huisinga 5
The potential
external exposure
systemic exposure (parent + metabolite)
exposure at site of action
effect
PBTK
MBTD Important to consider • variability • uncertainty • species differences • in vitro-in vivo differences
Most critical bottleneck for application: availability of parameter values
Prof. Wilhelm Huisinga 6
• Cell-culture in vitro assay data
à Conclusions for toxicological risk assessment? • Link from external exposure to systemic concentration and/or concentration at
target site? • Measure of exposure: Cmax, AUC, ...? Parent compound or metabolite?
Toxicity measured in in vitro assays
concentration of xenobiotic
mea
sure
of
toxi
city
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The structure of physiologically-based toxicokinetic models
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PBTK modelling
• Main features: — mechanistic model of principal ADME processes: (Absorption, Distribution, Metabolism, and Excretion) — compartments have anatomical interpretation — parameterized by physiological, anatomical and compound-specific data
• Long history in toxicokinetics — Teorell (1937) first PBPK model of therapeutically important, non-volatile chemical — Review: Gerlowski & Jain, PBPK modelling: Principles and applications, J Pharm Sci 72
(10), 1983
• More recent history in drug discovery and development — predominantly since 2000 due to large amount of parameters needed — breakthrough with seminal papers by Poulin&Theil, J Pharm Science (2000-2002)
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Biological complexity
Molecular dynamics
Systems biology
Toxicokinetics
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• Top down approach — organs, tissue and other spaces, interconnected by the blood flow
— Mass balance equations (ODEs) for concentrations in tissues/organs
Physiologically based pharmacokinetic models
Poulin & Theil, J Pharm Sci. (2002); Luepfert & Reichel, Chem Biodiv, (2005); Von Kleist, & Huisinga, J Pharmacokinet Pharmacodyn (2007)
Prof. Wilhelm Huisinga 11
Mass balance differential equations for each tissues/organ
Well-stirred tissue model:
VtisddtCtis =Qtis ! Cin "
Ctis
Ktis
#
$%
&
'("CLint !Ctis
inflowing blood conc.
out-flowing blood conc.
ssblood
sstistis C
CK
,
,=
Steady-state tissue-to-blood partition coefficient:
Prof. Wilhelm Huisinga 12
Mass balance differential equations for lung
Rate of change in lung:
Blood:air partition coefficient
alveolar space BP
PQCin Cout
Qco
Cven Cart
Pblo:air =Cart
Cout
Poulin & Krishnan, Toxicol Appl Pharmacol (1996)
alveolare ventilation rate
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Parameterization and parameters sources
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A rich source of data
(human: adult and children)
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Accounting for inter-individual variability
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A rich source of data
(animals: mice and rats)
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Parameterization of PBPK models
Tissue-to-blood partition coefficient:
Species specific • blood flows, organ
volumes
Drug specific • intrinsic clearance (CLint) • tissue-to-blood partition
coefficients • Administration (dose,
route, etc) ssblood
sstistis C
CK
,
,=
Rate of change in tissue:
VtisddtCtis =Qtis ! Cin "
Ctis
Ktis
#
$%
&
'("CLint !Ctis
inflowing blood conc.
out-flowing blood conc.
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A-priori prediction of partition coefficients
tissue
• Idea: Consider tissue as composition of constituents important for xenobiotic distribution
tissue constituents
“Kunst aufgeräumt“ by Ursus Wehrli neut
ral l
ipid
s
wat
er
phos
phol
ipid
s
prot
eins
etc
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• Ansatz based on mass balance equation
More mathematical
neut
ral l
ipid
s
inte
rsti
tial
wat
er
phos
phol
ipid
s
bind
ing
prot
eins
cellu
lar
wat
er
in vitro assay Octanol
Water up
nloctanol: C
CCCP
wwo ≈=
Approximate partition coefficients based on in vitro data
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Hepatic metabolism
VtisddtCtis =Qtis ! Cin "
Ctis
Ktis
#
$%
&
'("CLint !Ctis
intrinsic hetpatic clearance (potentially also saturable)
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Determining hepatic intrinsic clearance from in vitro data
• Hepatocyte assay
• Microsomal assay
• Scaling approach to hepatic intrinsic clearance
• with scaling factors
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Parameterization of PBPK models
Species specific • blood flows, organ
volumes • tissue composition data
Drug specific • intrinsic clearance CLint • blood:plasma ratio B:P • fraction unbound fuP • octanol-water coeff Pow • pKa value
• Administration (dose,
route, etc) ssblood
sstistis C
CK
,
,=
Tissue-to-blood partition coefficient:
Poulin/Theil (2000), Rodgers/Rowland (2005), Schmidt (2008)
Rate of change in tissue:
VtisddtCtis =Qtis ! Cin "
Ctis
Ktis
#
$%
&
'("CLint !Ctis
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Example
Prof. Wilhelm Huisinga 24
Example
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Example: exposure of styrene at 100 ppm for 8h
0 5 10 150
2
4
6
8exposure of styrene at 100 ppm for 8 hours
time [h]
conc
entra
tion
[mg/
l] in
arte
ry
newborn1year5years10years15yearsadult
0 5 10 150
5
10
15
20exposure of styrene at 100 ppm for 8 hours
time [h]
conc
entra
tion
[mg/
l] in
ske
leto
n
newborn1year5years10years15yearsadult
à different concentrations and profiles in different tissues/organs
0 5 10 150
20
40
60
80exposure of styrene at 100 ppm for 8 hours
time [h]
conc
entra
tion
[mg/
l] in
fat
newborn1year5years10years15yearsadult
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Non-linear relationship between external and systemic exposure
• Underlying reason: saturable metabolism
1 ppm 100 ppm
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Exposure ratio Child:Adult depending on external exposure (at 8h)
• exposure ratios also depend on time. • Sensitivity analysis showed that predictions are most sensitive to alveolar
ventilation rate with 20% change of Q_p à 14% change in ratio(newborn)
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Further examples
Gentry, Clewell, Anderson, ENVIRON, manuscript
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The potential
external exposure
systemic exposure (parent + metabolite)
exposure at site of action
effect
PBTK
MBTD Important to consider • variability • uncertainty • species differences • in vitro-in vivo differences
Most critical bottleneck for application: availability of parameter values
Prof. Wilhelm Huisinga 30
• Gerlowski & Jain, PBPK modelling: Principles and applications, J Pharm Sci 72 (10), 1983
• Poulin & Krishnan/Theil, 1995-2002 • K. Abraham, H. Mielke, W. Huisinga and U. Gundert-Remy, Elevated Internal
Exposure of Children in Simulated Acute Inhalation of Volatile Organic Compounds: Effects of Concentration and Duration, Arch Toxicol 79 (2005)
• M. Reddy et al, Physiologically-based Pharmacokinetic Modeling, Wiley 2005 • WHO, Characterization and Application of PBPK models in Risk Assessment,
2010 • H. Mielke, U. Gundert-Remy, Physiologically Based Toxicokinetic Modelling as a
Tool to Support Risk Assessment: Three Case Studies, J Toxicology, 2012
• and many more.
Some references
Prof. Wilhelm Huisinga 31
Acknowledgement
• U. Gundert-Remy (Berlin) • K. Abraham, H. Mielke (BfR, Berlin)
• For information:
Farbe/colour:PANTONE 288 CV
PhD Program PharMetrX, bridging pharmacy and mathematics at the Freie Universität Berlin and the Universität Potsdam/Germany, supported by