Institute of Physics and Biophysics
Helmut SchöllnbergerRonald E.J. Mitchel
Nonlinear Dose-Response MechanismsSimulation with Bio-Mathematical Models
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Contents
Introduction to the State Vector Model
Detrimental bystander effects for chromosome aberrations
Protective apoptosis-mediated BE for neoplastic transformation
Update on studies with Two-Stage Cancer model
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State Vector ModelFor neoplastic transformation
initiationvia chromosome translocation
promotionclonal expansion of I-cellsloss of contact inhibition
DSB repair
cell killing – dose rate dependent
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State Vector Model
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Detrimental bystander effects
Included in a dose-dependent way – strongesteffect at low doses
New bystander rates:
1)
k01b_by ×
exp(-λ1by ×
D)
2)
k01r_by ×
DR
×
exp(-λ2by ×
D)
3) (1+km_by
×
exp(-λ2by ×
D))
k01b_by = k01r_by = km_by = 0 at D = 0
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Data by Nagasawa and Little Mutation Research 2002
CHO and xrs-5 cells, α-particles,
total chromosome aberrations
First, fit model without BE to control and high dose data
Then, fit model with BE to all data
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Data by Nagasawa and Littleα-particle irradiation of CHO and xrs-5 cells
Dose (Gy)
0.0 0.4 0.8 1.2 1.6 2.0
Tota
l Chr
omos
ome
Aber
ratio
ns p
er C
ell
0
1
2
3
4
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Fit results
Approaches 1) and 3) worked equally well
Approach 2) did not work initiation due to BE ismostly post-exposure (as expected)
To fit xrs-5 data apply reduction factor for DSB repair rates
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Bystander-induced apoptosisIs a protective effectDr. Georg Bauer (Anticancer Res 2000)
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Bystander-induced apoptosis For low-LET radiation
Protective Apoptosis-Mediated process (PAM), B.R. Scott et al. (2003)
PAM can eliminate cells in State 4
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Bystander-induced apoptosis
PAM = 0 at D = 0PAM = 0 during irradiationPAM activated by 1 mGy low-LET radiationPAM activated for various times after irradiationPAM effective at low doses –no effect at D
> 200 mGy
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Data by Redpath et al. Radiat. Res. 2001
CGL1 cells, γ-rays, neoplastic transformation
Irradiation period: 3.3 mGy/min for D ≤ 100 mGycell doubling time of 20 hrs
1 day holding period: 20 hrs10 days exponential growth: 20 hrsConfluent growth until day 26: 38 days
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Fit approach
TF/SC =
Fit model without PAM to control and high dose data
for immediate and delayed plating simultaneously
Forward simulation without PAM to all data pointsfor immediate plating
Fit model with PAM to all data points for delayedplating 1 free parameter: kap
2 free parameters: kap
and tap_off
)()()()()()()(
432110
4
endendendendnsendsend
end
tNtNtNtNtNtNtN
+++++
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Data by Redpath et al. Forward simulation
Immediate plating
Dose (Gy)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Tran
sfor
mat
ion
Freq
uenc
y pe
r Sur
vivi
ng C
ell (
x105 )
0
2
4
6
8
10
0.000 0.005 0.0100
1
2
3
4
5
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Data by Redpath et al. Fit with two free parameters
Delayed plating
Dose (Gy)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Tran
sfor
mat
ion
Freq
uenc
y pe
r Sur
vivi
ng C
ell (
x105 )
0
2
4
6
8
10
0.000 0.005 0.0100
1
2
3
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Fit results
kap = 0.024/day How many State 4 cells killedat day 26 after 100 mGy?
Simulation performed starting with 1 cell: N4 (26) - N4 (26;kap
=0) = 9 cells
N0 (26) + N1s (26) +…+ N4 (26) = 8⋅105
tap_off = 22 daysJamali and Trott (1996): two week induction of apoptosis after 1 Gy X-irradiation
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Data by Miller et al. Radiat. Res. 1995
200 keV/μm
Dose (Gy)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Tran
sfor
mat
ion
Freq
uenc
y pe
r Sur
vivi
ng C
ell
0.0000
0.0002
0.0004
0.0006
0.0008
0.0010
0.0012
0.0014
0.0016
α-particle irradiation (150 keV/μm) of C3H 10T1/2 cells
Dose (Gy)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Tran
sfor
mat
ion
Freq
uenc
y pe
r Sur
vivi
ng C
ell
0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
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Conclusions
SVM can describe detrimental and protectivebystander effects
The experimentally proven phenomenon of bystander-induced apoptosis can explain protectiveeffects of low doses of low-LET radiation
SVM can also explain LNT-shaped data sets
Work towards a model than contains all essential mechanisms that work at low doses: inducible repairand radical scavenging, bystander effects …
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Four age-independent stochastic rates (μ1, μ2, α, β)
μ1 a function of dose-rate - also included endogenous DNA damage
Two Stage Clonal Expansion Model (TSCE)
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Total absorbed dose delivered in 75 years [mGy]
0 100 200 300 400 500 600 700 800 900 1000
Life
time
prob
abili
ty fo
r lun
g ca
ncer
at 7
5 ye
ars
10-5
10-4
10-3
10-2
Lifetime probability for lung cancer Low-LET radiation at low dose rates
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Total absorbed dose delivered in 75 years [mGy]
0 200 400 600 800 1000
Life
time
prob
abili
ty fo
r lun
g ca
ncer
at 7
5
10-5
10-4
10-3
10-2
G = F = const. = 1Gmax = Fmax = 1.4Gmax = Fmax = 3Gmax = Fmax = 5
Lifetime probability for lung cancer With repair and scavenger induction
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Rossi and Zaider: “Radiogenic lung cancer: the effects of low doses of low LET radiation” REB 1997
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Rate of change in the expected number of simple or complex lesions per cell at time t
-∞
birth Δt 75
30
)()( tLDdt
tdLii
radi
endoi
i λ−Σ+Σ=•
Mutation models for high dose rates
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)()(
)()(
)(1 tLLG
tLLG
t clclcl
clslsl
sl
sl λϕ
+λϕ
∝μ
ϕi
probability ith type (simple or complex) of lesion is misrepaired
Misrepair probability modifiedwith..
[ ])(11)( tLeLG Δ−−+= γδ
age (yrs)30.000 30.002 30.004
G(L
)
0.0
0.5
1.0
1.5
2.0
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[ ])(11)( tLeLG Δ−−+= γδ
Dx = 100 mGy
Δt = 1 day
dose (mGy)
0 50 100 150 200 250 300
L i( t)
- Li( 0
)
0
2
4
6
8
10
12
14
Lsl(t)-Lsl(0)Lcl(t)-Lcl(0)
•
bD = 3 mGy/yr
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dose (mGy)
0 50 100 150 200 250 300 350
μ 1
0.0
2.5e-6
5.0e-6
7.5e-6
1.0e-5without repair inductionwith repair induction
age (yrs)
30.000 30.002 30.004
μ 1
0.0
2.5e-6
5.0e-6
7.5e-6
1.0e-5without repair inductionwith repair induction
)()(
)()(
)(1 tLLG
tLLG
t clclcl
clslsl
sl
sl λϕ
+λϕ
∝μ
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AcknowledgementsCollaborator: Dr. Robert D. StewartAustrian Science Foundation FWF (project P18055-N02)RISC-RAD project, EC Contract No. FI6R-CT-2003-508842EU Marie Curie Individual Fellowship, EC Contract No. FIGH-CT-2002-50513Marie Curie European Reintegration Grant, EC Contract No. MERG-CT-2004-006610Atomic Energy of Canada LimitedUS Department of Energy, Grant Nos. DE-FG02-03ER63541 and DE-FG02-03ER63665
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