Models for cell survival



A set of models for cellular survival after irradiation is simply presented.


   THEORY
MODEL
REFERENCES
SURVIVAL FUNCTION
VARIABLES
TARGET
THEORY

Single-hit

Lea
(1955)


S = e-D / D0

- Dose


Multi-target single-hit
S = 1- (1- e-qD)n
- Dose
- Probability to hit a target
- Total number of targets
- Number of targets hit

Multi-target single-hit
S = e-q1D  [ 1- (1- e-qn D)n ]


Revised model
Sigle-target multi-hit
S= e-ßD*D


Single-target two-hits
Joiner & Johns


S=e-αR [1 + ( αS / αR -1) e-D/Dc] D–ß D 




MOLECULAR
THEORY

Radiation action
Chadwick and Leenhouts
(1981)
S = e–p ( αD + ßD  )
- Dose
- Number of times a target is hit
- Conditional probability function
Linear-quadratic model
Dual radiation action
Kellerer and Rossi
(1971)
S = S0e- k (ξ D + D ) 
- Dose
- Biological effectiveness factor
- Fraction of dose related to SSBs and to DSBs
- Unrestored fraction of bonds
- Effectiveness factor

Repair-misrepair
Tobias et al.
(1980)

 
S = e-αD[1+(αDT/ε)]ε
- Dose
- Max time for repair
- Linear repair constant
- Quadratic repair constant
- Probability for linear repair
- Probability for quadratic repair
Linear repair - quadratic misrepair
Repair-misrepair
S = e-αD[1+(αD/ε)]εΦ
Linear repair - misrepair
Lethal-potentially lethal
Curtis
(1986)
  
S=exp[-NTOT[1+ NPL /
[ε (1-e-εBAtr)] ]ε ]




- Dose
- Max time for repair
- Number of lethal lesions
- Number of potentially lethal lesions
- Constants related to lesion processes
- Constants related to repair processes

Lethal-potentially lethal  
S = e-ηAC D
Low dose approximation
Lethal-potentially lethal
 - ln[ S(t)] =
(
ηAC + ηAB) D–ε ln[1 +(ηABD/ε)(1–e-εBA tr)]
High dose approximation
Lethal-potentially lethal - ln[ S(t)] =
(
ηAC + ηAB e-εBAtr ) D + (η2AB/2ε)(1–e-εBA tr)2 D2]
Linear-quadratic approximation


Last modified 18 January 2005 - Barbara Mascialino