A%20Biologically-Based%20Model%20for%20Low-Dose%20Extrapolation%20of%20Cancer%20Risk%20from%20Ionizing%20Radiation

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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

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Whats our task? Extrapolate downwards in dose
and dose-rate
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Having trouble finding the right functional form?
No problem. We have in vitro studies to show us
that.
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Cells also die from radiation, so we need to
account for that
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Just use these to create a phenomenological model
PTSC(D) aD ßD2
S(D) e-kD
PT(D) (aD ßD2) x e-kD
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So whats the big deal? Just fit it!
in vitro Kd Fitted Kd
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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

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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)

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Then lets get a generic modeling framework
Exposure conditions
Environmental conditions
Deposition and clearance
Dose distribution
Dose- response
Probability of effect
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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

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The multi-stage nature of cancer
Initiation Promotion Progression Cell Death
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The state vector model
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The Mathematical Development of the SVM

• Let Ni(t) be the number of cell in State i at any
  time t
• Vector represents the state of
  the
• cellular community where
• The total cells in all states is denoted
• Transformation frequency is calculated by
• Six Differential equations describe the
  movement of cells through states
• Example

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And now for some parameter values chromosomal
aberrations
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Rate constants for repair rates and
transformation rate constants.
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Inactivation rate constants
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Then for promotion removal of contact inhibition
Showing Complete removal of cell-cell contact
inhibition
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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)
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Model fit to in vitro data
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Sensitivity to Pci value
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Low dose behavior (no adaptive response)
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Low dose behavior (with adaptive response)
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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
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The rat data (Battelle in circles and Monchaux et
al in triangles)
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So, does this work for rats??
Well, not so much..
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With dose variability
PC(D) ? PDF(D) (aD ßD2) e-kD dD
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Incorporating dose variability
GSD 1, 5, 10
Empirically lognormal with GSD 8
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Deterministic or stochastic?
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Deterministic or stochastic?
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Back to the issue of differentiation, Rd/s in the
kinetics model
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Changes in Rd/s
1, 2, 4
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Fits to mining data
With depth-dose information Without depth-dose
information
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Inverting the dose-rate effect
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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

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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)

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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

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Why does it not work (continued)??

• Dose distributions different at the new level of
  biological organization we account for the
  distributions, but we dont 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