Cell survival-curve

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.