A Biologically-Based Model for Low-Dose Extrapolation of Cancer Risk
from Ionizing Radiation
Doug Crawford-Brown
School of Public Health
Director, Carolina Environmental Program
What’s our task? Extrapolate downwards in dose and dose-rate
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WLM
tum
or
inci
den
ce
Having trouble finding the right functional form? No problem. We
have in vitro studies to show us that.
0.00E+00
5.00E-04
1.00E-03
1.50E-03
2.00E-03
2.50E-03
3.00E-03
3.50E-03
0 0.2 0.4 0.6 0.8 1 1.2
Dose (Gy)
TF
/S
Cells also die from radiation, so we need to account for that
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0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1 1.2
Dose (Gy)
S(D
)
Just use these to create a phenomenological model
PTSC(D) = αD + βD2
S(D) = e-kD
PT(D) = (αD + βD2) x e-kD
So what’s the big deal? Just fit it!
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tum
or in
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nce
in vitro Kd “Fitted” Kd
Why does it not work??
• Model mis-formulation even at lower level of biological organization
• New processes appear at the new level of biological organization (emergent properties)
• Processes disappear at the new level of biological organization
• Incorrect equations governing processes• Parameter values differ at the new level of
biological organization
Why does it not work (continued)??
• Dose distributions different at the new level of biological organization
• Computational problems somewhere• Anatomy, physiology and/or morphometry differ
at the new level of biological organization• Errors in the data provided (exposures,
transformation frequency, probability of cancer, etc)
Then let’s get a generic modeling framework
Exposure conditions
Environmental conditions
Deposition and clearance
Dose distribution
Dose-response
Probability of effect
The environmental, exposure and dosimetry conditions
• In vitro doses are uniform as given by the authors, and at the dose-rates provided
• Rat exposures are from Battelle and Monchaux et al studies, under the conditions indicated by the authors
• Human exposures are from the uranium miner studies in Canada
• Rat and human dosimetry models using Weibel bifurcating morphology
• Uses mean bronchial dose in TB region, or dose distributions throughout the TB region and depth in the epithelium
The multi-stage nature of cancer
Initiation
Promotion
Progression
Cell Death
The state vector model
State 0
State 1S
State 6
State 1NS
State 2 State 3
State 4State 5
k23
k34
P45k56
kRS
kRNS
kRNS
kRS
ks
kNS
kNS
kS
State 7k67
k54
)()()( 111 tNtNtN nss
333432233 NkNkNkNk
dt
dNdmi
)()()()()()( 43210 tNtNtNtNtNtNT
)(
)()( 4
4 tN
tNtf
T
3
The Mathematical Development of the SVMLet Let NNii(t) (t) be the number of cell in State be the number of cell in State ii at any time at any time tt::
• Vector Vector represents the state of the represents the state of the cellular community wherecellular community where
• The total cells in all states is denoted: The total cells in all states is denoted:
• Transformation frequency is calculated by:Transformation frequency is calculated by:
• Six Differential equations describe the movement of cells through Six Differential equations describe the movement of cells through statesstates
Example: Example:
)](),(),(),(),([ 43210 tNtNtNtNtN
And now for some parameter values: chromosomal aberrations
Dose (Gy)
0.0 0.4 0.8 1.2 1.6 2.0
To
tal C
hro
mo
som
e A
ber
rati
on
s p
er C
ell
0
1
2
3
4
Rate constants for repair rates and transformation rate constants.
0.00E+00
5.00E-04
1.00E-03
1.50E-03
2.00E-03
2.50E-03
3.00E-03
3.50E-03
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Dose (Gy)
TF
/S
Inactivation rate constants
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0.8
1
1.2
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Dose (Gy)
S(D
)
Then for promotion: removal of contact inhibition
I
D
DD
DD
DShowing: Complete removal of
cell-cell contact
inhibition
6 6)(1)(6
cipcipcip
ci
tptpp
F
So, does this work for x-rays? The in-vitro data on transformation
Pooled data from many experiments for the transformation rate for single () and split (O) doses of
X-rays (Miller et al. 1979)
Model fit to in vitro data
Sensitivity to Pci value
Low dose behavior (no adaptive response)
A
Dose (Gy)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Tra
ns
form
atio
n F
req
uen
cy
per
Su
rviv
ing
Ce
ll (x
105)
0
2
4
6
8
10
0.000 0.005 0.0100
1
2
3
4
5
Low dose behavior (with adaptive response)
B
Dose (Gy)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Tra
nsf
orm
atio
n F
req
ue
ncy
pe
r S
urv
ivin
g C
ell
(x1
05)
0
2
4
6
8
10
0.000 0.005 0.0100
1
2
3
But does it work for in vivo
exposures to high LET radiation with
very inhomogeneous
patterns of irradiation?
Helpful scientific picture from EPA web site
The rat data (Battelle in circles and Monchaux et al in triangles)
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Mean Dose (Gy)
P(D
)
So, does this work for rats??
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Mean Dose (Gy)
P(D
)
Well, not so much……..
With dose variability
PC(D) = ∫ PDF(D) * (αD + βD2) * e-kD dD
Incorporating dose variability
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Mean Dose (Gy)
P(D
)
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0.250.3
0.35
0.4
0.45
0.5
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Mean Dose (Gy)
P(D
)
0
0.05
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0.15
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0.25
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0.35
0.4
0.45
0 100 200 300 400 500
Mean Dose (Gy)
P(D
)
GSD = 1, 5, 10
Empirically: lognormal with GSD = 8
Deterministic or stochastic?
State 0
State 1S
State 6
State 1NS
State 2 State 3
State 4State 5
k23
k34
P45k56
kRS
kRNS
kRNS
kRS
ks
kNS
kNS
kS
State 7k67
k54
Deterministic or stochastic?
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Mean Dose (Gy)
P(D
)
Back to the issue of differentiation, Rd/s in the kinetics model
Changes in Rd/s
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Mean Dose (Gy)
P(D
)
1, 2, 4
Fits to mining data
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WLM
tum
or in
cide
nce
With depth-dose information Without depth-dose information
Inverting the dose-rate effect
________________________________________________________________ Exposure (WLM) Exposure rate (WLM/yr) Lung cancer risk ________________________________________________________________ 2.7* 0.007 200 10 0.006
0.27* 0.030 20 10 0.035
________________________________________________________________ *based on an exposure time of 73 years
Conclusions (continued)
• Good fit to the in vitro data, even at low doses if adaptive response is included (IF you believe the low-dose data!)
• Reasonable fit to rat and human data at low to moderate doses, but only with dose variability folded in
• Best fit with Rd/s included to account for differentiation pattern in vivo
Conclusions
• Under-predicts human epidemiological data at higher levels of exposure
• Under-predicts rat data at higher levels of exposure, especially for Battelle data (not as bad for the Monchaux et al data)
Why did it not work??
• Model mis-formulation even at lower level of biological organization: compensating errors that only became evident at higher levels of biological organization
• New processes appear at the new level of biological organization: clusters of transformed cells needed to escape removal by the immune system
• Processes disappear at the new level of biological organization: cell lines too close to immortalization to be valid at higher levels
• Incorrect equations governing processes: dose-response model assumes independence of steps
• Parameter values differ at the new level of biological organization: not true for cell-killing, but may be true for repair processes
Why does it not work (continued)??
• Dose distributions different at the new level of biological organization: we account for the distributions, but we don’t know the locations of stem cells
• Computational problems somewhere: what exactly are you suggesting here (but perhaps a problem of numerical solutions under stiff conditions)???
• Anatomy, physiology and/or morphometry differ at the new level of biological organization: we think we are accounting for this
• Errors in the data provided: well, not all mistakes are introduced by theoreticians