Contents
Toxicokinetics The one-compartment model and diffusion Effects of composition and reproduction
Complications: toxicants in soil and feeding
externalconcentration
(in time)
toxico-kineticmodel
toxico-kineticmodel
“Biology-based” modelling
internalconcentration
in time
process modelfor the organism
process modelfor the organism
effects onendpoints
in timetoxicokinetics
toxicodynamics
externalconcentration
(in time)
toxico-kineticmodel
toxico-kineticmodel
“Biology-based” modelling
internalconcentration
in time
toxicokinetics
Toxicokinetic modelling Quite popular in
(eco)toxicology and pharmacology
Models differ in complexity
Start from diffusion
Let’s assume …• well-mixed homogeneous cube with water, in a solution• cube has a semi-permeable membrane• exchange proportional to area and concentration difference
Start from diffusion
Let’s change the cube …• the same cube, now filled with oil ...• correct one concentration with partition coefficient between
oil and water
Start from diffusion
Let the cube grow …• without changing the shape• leads to dilution and change in surface:volume ratio
Diffusion in organisms
Let’s move to an organism …• can we talk about internal ‘concentration’?• can we assume it is ‘well-mixed’?• what is the surface area for exchange?• when size and composition is constant …
Scaled concentration
Problem• often, internal concentrations are not measured …• or not relevant for effects
Effects data contain information ...• effects over time provides info on build up of body residue• but, no information about absolute levels
co
nce
ntr
atio
n
external
scaled internal
time
Adding some realism
Organisms may grow ...• dilution of concentration• change of surface:volume ratio
externalconcentration
(in time)
toxico-kineticmodel
toxico-kineticmodel
“Biology-based” modelling
internalconcentration
in time
process modelfor the organism
effects onendpoints
in time
body sizegrowth
Active uptake
Uptake/elimination of chemicals may be active• ions such as metals, nutrients• chemicals may be metabolised, or bound
No difference as long as:• uptake flux external concentration• elimination flux internal concentration
But ...• active processes can saturate• possible link to metabolic processes
More realism
eggseggsbufferbufferstructurestructure
reservereserve
water
Body composition may change• reserve density changes with food level and toxicants• females build up a reproduction buffer
Females may reproduce• chemicals can be transferred to eggs
More realism
Assumptions• distribution chemical over internal compartments is fast• reserve, buffer and egg have same composition• only structure exchanges with environment• chemicals from buffer are transferred to egg
eggseggsbufferbufferstructurestructure
reservereserve
water
Reproduction buffer
Assumptions• chemical follows reserves associated with eggs• rest remains in buffer
bufferbuffer eggseggs
overheadoverhead
remainderremainderreservereservechemicalchemical
Simulations
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concentration structure
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concentration reserves
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concentration total
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concentration total
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cumul. reproduction
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concentration structure
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concentration reserves
time0 20 40 60
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concentration total
time
Simulations
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cumul. reproduction
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concentration structure
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concentration reserves
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concentration total
time
Reproduction buffer
Assumptions• chemical follows reserves associated with eggs• rest remains in buffer
bufferbuffer eggseggs
overheadoverhead
remainderremainder
Simulations
0 20 40 600
0.05
0.1
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0.2
structural length
time0 20 40 60
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physical length
time0 20 40 60
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cumul. reproduction
time
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5
10
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concentration structure
time0 20 40 60
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concentration reserves
time0 20 40 60
0
5
10
15
concentration total
time
Simulations
0 20 40 600
0.05
0.1
0.15
0.2
structural length
time0 20 40 60
0
0.05
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physical length
time0 20 40 60
0
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cumul. reproduction
time
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50concentration structure
time0 20 40 60
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time0 20 40 60
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50concentration total
time
Simulations
0 20 40 600
0.05
0.1
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structural length
time0 20 40 60
0
0.05
0.1
0.15
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physical length
time0 20 40 60
0
1000
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cumul. reproduction
time
0 20 40 600
5
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concentration structure
time0 20 40 60
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concentration reserves
time0 20 40 60
0
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concentration total
time
What happens in an egg?
During the embryonic phase …• mass is lost so concentration increases
• if PEV > 1, conversion reserve to structure increases concentration structure even more
• how does egg exchange toxicants with surroundings?
reservereserve
structurestructure
reservereserve
structurestructure
overheadsmaintenancewater
??
Assumptions realistic?
Difficult to say ... Most test setups avoid growth, reproduction and
changes in feeding status ...
Some support:• Russell et al 1999: lipid-normalised concentrations in fish
and eggs are similar• Daley et al 2009: fish eggs increase in fugacity of PCBs over
incubation
This extension takes the DEB assumptions to their logical consequences• with a minimum of additional parameters
externalconcentration
(in time)
toxico-kineticmodel
toxico-kineticmodel
“Biology-based” modelling
internalconcentration
in time
process modelfor the organism
effects onendpoints
in time
body sizegrowth
reservesreproduction ratebuffer handling
(and toxicant effects on them)
externalconcentration
(in time)
toxico-kineticmodel
toxico-kineticmodel
“Biology-based” modelling
internalconcentration
in time
process modelfor the organism
effects onendpoints
in time
More extensions?
Plenty of options to make it more complex …• uptake from food/inhalation• saturating uptake or elimination• biotransformation• more compartments (as in PBPK)• ...
Summarising
TK models range from simple to complex• simplest is scaled one-compartment model with constant
composition (1 parameter: ke)
DEB offers logical links to include effects of growth, reserve and reproduction• one-compartment model with varying parameters• TK becomes closely integrated with the DEB organism• toxicants can affect their own TK …