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

Having trouble finding the right functional form? No problem. We have in vitro studies to show us that.

Cells also die from radiation, so we need to account for that

Just use these to create a phenomenological model P TSC (D) = αD + βD 2 S(D) = e -kD P T (D) = (αD + βD 2 ) x e -kD

So what’s the big deal? Just fit it! in vitro K d “Fitted” K d

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

3 The Mathematical Development of the SVM Let N i (t) be the number of cell in State i at any time t: Vector represents the state of the Vector represents the state of the cellular community where cellular 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 states Six Differential equations describe the movement of cells through states Example: Example:

And now for some parameter values: chromosomal aberrations

Rate constants for repair rates and transformation rate constants.

Inactivation rate constants

Then for promotion: removal of contact inhibition I D D D D D D Showing: Complete removal of cell-cell contact inhibition

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 P ci value

Low dose behavior (no adaptive response)

Low dose behavior (with adaptive response)

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)

So, does this work for rats?? Well, not so much……..

With dose variability P C (D) = ∫ PDF(D) * (αD + βD 2 ) * e -kD dD

Incorporating dose variability GSD = 1, 5, 10 Empirically: lognormal with GSD = 8

Deterministic or stochastic?

Back to the issue of differentiation, R d/s in the kinetics model

Changes in R d/s 1, 2, 4

Fits to mining data With depth-dose information Without depth-dose information

Inverting the dose-rate effect

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 R d/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