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Cell Survival Curves
Abish Adhikari,Resident, Radiation/Oncology
NAMS, Kathmandu
Defination
• “describes the relationship between the radiation dose and the proportion of cells that survive.”
• Death could be either ‘Reproductive Death’ or ‘Functional Death’
• ~100Gy is needed to ‘Destroy’ the cell, but only ~2Gy to functionally kill the cell.
Survival
• The capability of a cell to divide and form a colony is the sure sign of survival.
• Tissue chopped → Trypsin→ Single cell suspension → Electronic Counter
• Cultivation → Incubation → Colonies Counting
Some Formulae
Some Formulae
Shape of the Curve
Shape of the Curve
→
→
Survival Curve
• Dose plotted on a linear scale and surviving fraction on a logarithmic scale.
• At High LETs, such as α-particles or low-energy neutrons, the curve is a straight line.
• For sparsely ionizing (low LET) radiations, such as x-rays -
Survival Curve
• Starts out straight with a finite initial slope; that is, the surviving fraction is an exponential function of dose.
• At higher doses, the curve bends.• At very high doses, the survival curve often
tends to straighten again; the surviving fraction returns to being an exponential function of dose.
Models of Description of the Curve
• Single-target Model• Multi-target Model• Linear Quadratics Model
Multi-Target Model
• Described in terms of an initial slope, D1, resulting from single-event killing;
• A final slope, D0, resulting from multiple-event killing;
• And some quantity (either n or Dq) to represent the size or width of the shoulder of the curve.
Multi Target Model• The quantities D1 and D0 are the reciprocals of the
initial and final slopes. • It is the dose required to reduce the fraction of
surviving cells to 37% of its previous value. 1 to 0.37 (i.e. to e-1)
• For oxygenated mammalian cells, D0 is about 150 rads (1.5 Gy).
• Dq defined as the dose at which the straight portion of the survival curve, extrapolated backward, cuts the dose axis drawn through a survival fraction of unity.
three parameters, n, D0, and Dq, are related by the expression
logen = Dq/D0
Linear-Quadratic Model
• assumes that there are two components to cell killing by radiation,
• one that is proportional to dose (Linear)• one that is proportional to the square of
the dose. (Quadratic)
• many chromosome aberrations are result of two separate breaks. Most of them lethal.
Linear Quadratic Curve
• The ‘bendiness’ is determined by α/β ratio• S = e-αD-βD2
• S is the fraction of cells surviving a dose D, • α and β are constants. • If at a dose D, αD = βD2 then: D = α/β
• SF = e-(αD+βD2)
• D is the dose in Gy, • α is the cell kill per Gy of the initial linear
component (on a log-linear plot) and • β the cell kill per Gy2 of the quadratic
component of the survival curve.
Survival curve for HeLa cells in culture exposed to x-rays. Characteristically, this cell line has a small initial shoulder
Bystander Effect
• Defined: “the induction of biologic effects in cells that are not directly traversed by a charged particle, but are in close proximity to cells that are.”
• ~30% of bystander cells can be killed in this situation.
• Presumably due to cytotoxic molecules released into the medium.
Apoptotic and Mitotic Death
• Greek word meaning “falling off,” as in petals from flowers or leaves from trees.
• First, apoptosis after radiation seems commonly to be a p53-dependent process.
• Mitotic death is common: Cells die attempting to divide because of damaged chromosomes.
• S=e-(αM
+αA
)D-βM
D2
• S is the fraction of cells surviving a dose D,• αM and αA describe the contributions to cell
killing from mitotic and apoptotic death that are linear functions of dose,
• βM describes the contribution to mitotic death that varies with the square of the dose.
Extra-Radiosensitive
• Ataxia telangiectasia (AT)• Basal cell nevoid syndrome• Cockayne's syndrome• Down's syndrome• Fanconi's anemia• Gardner's syndrome• Nijmegan breakage syndrome• Usher's syndrome
EFFECTIVE SURVIVAL CURVE FOR A MULTIFRACTION REGIMEN
• Multifraction regimens are used most often.• “If a radiation dose is delivered in a series of
equal fractions, separated by sufficient time for repair of sublethal damage to occur between doses, the effective dose-survival curve becomes an exponential function of dose.” – thus making a straight line.
• The biological effect (E) per fraction (n) of fractional dose (D) can be expressed as:
• En = (αD+βD2)• So, Biologically Effective Dose
BED = E/α = nD (1 + (D / (α/β)))
• For calculation purposes, it is often useful to use the D10, the dose required to kill 90% of the population. For example:
• D10 = 2.3 × D0
in which 2.3 is the natural logarithm of 10.
Radiation & Micro-organismsA, mammalian cells;B, E. coli; C, E. coli B/r; D, yeast; E, phage staph E; F, B. megatherium; G, potato virus; H, Micrococcus radiodurans.
if radiation is used as a method of sterilization, 20,000 Gy necessary.