Transcript A Biologically-Based Model for Low-Dose Extrapolation of Cancer Risk from Ionizing Radiation Doug Crawford-Brown

A Biologically-Based Model for LowDose 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
0.8
0.7
tumor incidence
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2000
4000
6000
WLM
8000
10000
Having trouble finding the right
functional form? No problem. We
have in vitro studies to show us that.
3.50E-03
3.00E-03
TF/S
2.50E-03
2.00E-03
1.50E-03
1.00E-03
5.00E-04
0.00E+00
0
0.2
0.4
0.6
Dose (Gy)
0.8
1
1.2
Cells also die from radiation, so we
need to account for that
1.2
1
S(D)
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
Dose (Gy)
0.8
1
1.2
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!
0.7
“Fitted” Kd
in vitro Kd
0.6
tumor incidence
0.5
0.4
0.3
0.2
0.1
0
0
1000
2000
3000
4000
5000
WLM
6000
7000
8000
9000 10000
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
Probability
of effect
Doseresponse
Dose
distribution
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
kRNS
kRS
ks
State 1S
kNS
k23
State 0
State 2
kNS
State 1NS
State 3
kS
k34
kRNS
kRS
k67
State 7
P45
k56
State 6
State 5
State 4
k54
The Mathematical Development of the SVM
Let Ni(t) be the number of cell in State i at any time t:
•
Vector [ N 0 (t ), N1 (t ), N 2 (t ), N3 (t ), N 4 (t )] represents the state of the
cellular community where N1 (t )  N1s (t )  N1ns (t )
•
The total cells in all states is denoted:
NT (t )  N 0 (t )  N1 (t )  N 2 (t )  N3 (t )  N 4 (t )
f 4 (t ) 
N 4 (t )
N T (t )
•
Transformation frequency is calculated by:
•
Six Differential equations describe the movement of cells through states
Example:
3
dN 3
 k 23 N 2  k mi N 3  k34 N 3  k d N 3
dt
Total Chromosome Aberrations per Cell
And now for some parameter
values: chromosomal aberrations
4
3
2
1
0
0.0
0.4
0.8
1.2
Dose (Gy)
1.6
2.0
Rate constants for repair rates and
transformation rate constants.
3.50E-03
3.00E-03
TF/S
2.50E-03
2.00E-03
1.50E-03
1.00E-03
5.00E-04
0.00E+00
0
0.2
0.4
0.6
Dose (Gy)
0.8
1
1.2
Inactivation rate constants
1.2
1
S(D)
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
Dose (Gy)
0.8
1
1.2
Then for promotion: removal of
contact inhibition
D
D
Showing:
Complete
removal of
cell-cell
contact
inhibition
D
I
D
D
D
 6 
p
6 p
F   p   p(t ) ci 1  p(t ) ci
ci p
 ci 
6
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
Transformation Frequency per Surviving Cell (x105)
Low dose behavior
(no adaptive response)
10
5
A
4
8
3
2
1
6
0
0.000
0.005
0.010
4
2
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Dose (Gy)
0.7
0.8
0.9
1.0
Transformation Frequency per Surviving Cell (x105)
Low dose behavior
(with adaptive response)
10
3
8
B
2
1
6
0
0.000
0.005
0.010
4
2
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Dose (Gy)
0.7
0.8
0.9
1.0
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)
0.45
0.4
0.35
P(D)
0.3
0.25
0.2
0.15
0.1
0.05
0
0
10
20
30
40
Mean Dose (Gy)
50
60
70
So, does this work for rats??
0.45
0.4
0.35
P(D)
0.3
0.25
0.2
0.15
0.1
0.05
0
0
5
10
15
20
25
Mean Dose (Gy)
Well, not so much……..
30
35
With dose
variability
PC(D) = ∫ PDF(D) * (αD + βD2) * e-kD dD
Incorporating dose variability
P(D)
GSD = 1, 5, 10
0.45
0.4
0.35
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
20
40
60
80
100
120
Mean Dose (Gy)
0.25
0.2
0.15
0.1
0.05
0.45
0
0.35
0.4
0
5
10
15
20
25
30
Mean Dose (Gy)
35
0.3
P(D)
P(D)
0.3
0.25
0.2
0.15
0.1
0.05
Empirically: lognormal
with GSD = 8
0
0
100
200
300
Mean Dose (Gy)
400
500
Deterministic or stochastic?
kRNS
kRS
ks
State 1S
kNS
k23
State 0
State 2
kNS
State 1NS
State 3
kS
k34
kRNS
kRS
k67
State 7
P45
k56
State 6
State 5
State 4
k54
Deterministic or stochastic?
0.45
0.4
0.35
P(D)
0.3
0.25
0.2
0.15
0.1
0.05
0
0
20
40
Mean Dose (Gy)
60
80
Back to the issue of differentiation,
Rd/s in the kinetics model
Changes in Rd/s
0.6
1, 2, 4
0.5
P(D)
0.4
0.3
0.2
0.1
0
0
20
40
Mean Dose (Gy)
60
80
Fits to mining data
With depth-dose information
Without depth-dose information
0.7
0.6
tumor incidence
0.5
0.4
0.3
0.2
0.1
0
0
1000
2000
3000
4000
5000
WLM
6000
7000
8000
9000 10000
Inverting the dose-rate effect
________________________________________________________________
Exposure (WLM)
Exposure rate (WLM/yr)
Lung cancer risk
________________________________________________________________
2.7*
0.007
10
0.006
0.27*
0.030
200
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: doseresponse 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