Description for a problem studied at the Virtual Physiological Human Network of Excellence Study Group
< http://www.maths-in-medicine.org/vph-noe/2009/radiotherapy-damage/ >
PROJECT: QUANTIFYING RADIATION-MEDIATED DAMAGE TO THE GUT
EPITHELIUM: APPLICATIONS TO CANCER RADIOTHERAPY
Prof. Alastair J. Munro1 and Dr. Ingeborg M.M. van Leeuwen1,2
1Department of Surgery and Oncology, Ninewells Hospital, University of Dundee
2Department of Microbiology, Tumour and Cell Biology, Karolinska Institute, Stockholm
Cancer therapy with drugs and/or radiation can damage the structure and functional integrity of the
gastrointestinal epithelium, the extent of the damage being dependent upon a number of identifiable
variables. Such damage is dose-limiting and limitations on dose may compromise the effectiveness of
treatment. All therapeutic schedules represent a pragmatic compromise between damage to tumour and
damage to normal tissues. There have been extensive studies on the kinetics of damage and repair of the
gastrointestinal epithelium following a variety of insults. Some of these data have already been incorporated
into mathematical models.
Figure 1: Normal colonic mucosa. The intestinal epithelium, which covers the luminal surface and lines the crypts,
resides on a basement membrane. Figure reproduced from Van Leeuwen et al (2009) Cell Prolif, in press.
(A) Microdissection image. The circular structures correspond to cross-sections of crypts; the space between these glands
contains connective tissue (the lamina propria), blood vessels and lymphatics. (B) Schematic of a colonic crypt.
ASSESSING DOSE-LIMITING DAMAGE IN THE GUT EPITHELIUM
Radiotherapy protocols are generally devised according to the tolerance of normal tissues directly exposed to
the beam. Recent experimental evidence suggest, however, that cells outside the exposure field are subject to
radiation-induced bystander effects, resulting from cell-cell and cell-matrix interactions. The spatial
propagation of bystander effects is particularly relevant at low doses, as under these conditions only a small
number of cells suffer a “direct hit”. We propose to use mathematical modelling to quantify such DNA-
damage-independent effects and estimate the resulting net tolerance of the normal tissue.
State-of-the-art in modeling radiation effects
The majority of studies on the mathematical modeling of the effects of radiation on living systems have use a
straightforward linear-quadratic (LQ) model of cell killing:
S(D) = exp(−α−βD2),
with S the survival function and D the radiation dose. This represents a pragmatic, but over-simplified,
approach with no robust mechanistic foundation. Radiation biologists have failed to exploit the richness of
modern mathematical techniques and we believe that we have identified an area, of direct clinical
importance, that is ripe for exploitation.
Questions/suggestions for the Study Group
• Gradually add new layers of complexity as follows: (1) nonspatial approach, (2) 1D epithelium (i.e. row
of cells), and (3) epithelium embedded in 3D tissue.
• Firstly build a biologically-based model describing DNA-damage-mediated radiation effects.
• Then, extend the model to account for DNA-damage independent effects.
• How could the model be used to distinguish between effects on normal and tumour tissues?
• Which parameters have the most dramatic influence on the radiation damage?
• Which parameters play a key role in defining the variation in radiation effects among patients?
Figure 2: Radiation effects.
* Green background: area covered (more or less) by the conventional cell-kill linear-quadratic equation
* White background: domains of radiation biology that are not covered adequately by the classical approach.
SOME RELEVANT PARAMETER VALUES
Human crypt Murine crypt Cell-cycle times Various Various
40-60 cells per crypt Average 21.9 cells per M-phase = 1 hour Colonic epithelium migrates at Spontaneous mutation rate =
side crypt side 5-10µm/h 10-9 per base per division
Total 2000 cells Total 235-250 cells G1-phase = 10-14 About 300 cells leave the human Methylation errors = 2×10-5 per
hours crypt per day CpG per division
Basement memb.: Average 18.3 cells per G2-phase = 2-4 hours Apoptotic cells are removed in 30-60 Human niche succession time =
50-100nm thick crypt circumference min 8.2 years
Renewal time = Renewal time = S-phase = 3-6 hours Standard radiotherapy regime for
4-6 days 3-5 days large bowel cancer: 45Gy in 25
fractions of 1.8Gy over 5 weeks
Most schedules currently used in clinical practice have been derived empirically and are employed in a
standard fashion, with little account taken of patient-to-patient variation. We suggest that it should be
possible, using available biological data in conjunction with mathematical modelling, to devise an approach
to treatment scheduling that is more individually based and takes account of patient-to-patient variation in
susceptibility to harm. In essence it may be possible to increase the intensity of scheduling for patients who
are at lower risk of treatment-related gastrointestinal damage and, conversely, decrease intensity for patients
considered to be particularly susceptible to the adverse effects of treatment.
• Feinendegen (2005) Significance of basic and clinical research in radiation medicine: challenges for the future, Br J Radiobiol
(Suppl 27): 185.
• O’Rourke et al (2009) Linear quadratic and tumour control probability in external beam radiotherapy, J Math Biol, in press.
• Mothersill & Seymour (2001) Review - radiation-induced bystander effects: past history and future perspectives, Radiat Res 155:
• Munro (2009) Bystander effects and their implications for clinical radiotherapy, J Radiol Protec: in press.
• Paulus et al (1992) A model of the control of cellular regeneration in the intestinal crypt after perturbation based solely on local
stem cell regulation, Cell Prolif 25: 559.
• Prise et al (2005) New insights on cell death from radiation exposure, Lancet Oncol 6: 520.
• Van Leeuwen et al (2006). Crypt dynamics and colorectal cancer: advances in mathematical modelling, Cell Prolif 39: 157.
• Roberts et al (1995) Deduction of the clonogen content of intestinal crypts: a direct comparison of two-dose and multi-dose
methodologies, Radiat Res 141: 303.
• Shuryak et al (2007) Biophysical models of radiations bystander effects: spatial effects in three-dimensional tissues, Radiat Res