Download Lecture 7 - Biology of Cancer

Models of Cell Survival
Lecture 7
Ahmed Group
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Lecture 7
Random nature of cell killing and Poisson statistics
Doses for inactivation of viruses, bacteria, and eukaryotic
cells after irradiation
Single hit, multi-target models of cell survival
Two component models
Linear quadratic model
Calculations of cell survival with dose
Effects of dose, dose rate, cell type
Ahmed Group
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Lecture 7
Random nature of cell killing and Poisson statistics
Doses for inactivation of viruses, bacteria, and eukaryotic
cells after irradiation
Single hit, multi-target models of cell survival
Two component models
Linear quadratic model
Calculations of cell survival with dose
Effects of dose, dose rate, cell type
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Modes of Radiation Injury
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Primarily by ionization and free radicals
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Low LET (X- and gamma-rays) damage by free radicals
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High LET (protons and a particles) damage by ionization
Energy released by ionization is 33 eV that is more than
sufficient to break a C=C bond that require 4.9 eV
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Resultant mode of inactivation
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There is no assay to differentiate the damage caused by
radiation-induced ionization or free-radicals
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Modifying the radiation effects by pre-exposing to
chemicals indicate primarily due to indirect action,
however, the damage produced by ionization is not
modifiable by chemicals
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The damage can cause cell death, prolonged cell cycle
arrest or reproductive death.
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Fate of Irradiated Cells
1. Division Delay
2. Interphase Death
3. Reproductive Failure
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(Dose = 0.1 to 10 Gy)
Apoptosis
Loss of clonogenicity
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Lecture 7
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Quantitation of cell killing and Poisson statistics
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Ionizations produced within cells by irradiation are distributed
randomly.
Consequently, cell death follows random probability statistics (Poisson
statistics), the probability of survival decreasing geometrically with
dose.
A dose which reduces cell survival to 50% will, if repeated, reduce
survival to 25%, and similarly to 12.5% from a third exposure. Thus, a
straight line results when cell survival from a series of equal dose
fractions is plotted on a logarithmic ordinate as a function of dose on a
linear abscissa.
The slope of such a semi-logarithmic dose curve could be described by
the D50, the dose to reduce survival to 50%, the D10, the dose to reduce
survival to 10%, or traditionally, by one natural logarithm, to e-1or
37%.
The reason for choosing Do to describe the slope of a dose survival
curve is that it represents one mean lethal dose, that is, the effect of
randomly distributing 100 lethal events among 100 cells.
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Lecture 7
Ahmed Group
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Lecture 7
Random nature of cell killing and Poisson statistics
Doses for inactivation of viruses, bacteria, and eukaryotic
cells after irradiation
Single hit, multi-target models of cell survival
Two component models
Linear quadratic model
Calculations of cell survival with dose
Effects of dose, dose rate, cell type
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Lecture 7
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Lecture 7
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Mammalian cells versus microorganisms
Mammalian cells are significantly more
radio-sensitive than microorganisms:
- Due to the differences in DNA content
- More efficient repair system
- Sterilizing radiation dose for bacteria is 20,000 Gy
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Chromosomal DNA is the principal target for
radiation-induced lethality
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Apoptotic and Mitotic Death
Apoptosis (Programmed Cell Death) was first described by Kerr et al. The
hallmark of apoptosis is DNA fragmentation.
Mitotic death is a common form of cell death from radiation exposure.
Death occurs during mitosis due to damaged chromosomes.
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Chromosomal aberrations and cell survival
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Survival curves for cell
lines of human and
rodent origin
A
B
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Radiation sensitivity profiles for cells of
human origin
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Categories of Mammalian Cell
Radiosensitivity
Cell Type
Properties
Examples
I. Vegetative
intermitotic cells
Divide regularly,
no differentiation
Erythroblasts,
Intestinal crypt cells,
Basal cells of oral
mucous membrane
II. Differentiating
intermitotic cells
Divide regularly,
some differentiation
between division
Spermatocytes, Oocytes,
Inner enamel of
developing teeth
III. Connective Tissue
Divide irregularly
Endothelial cells,
Fibroblasts
IV. Reverting postmitotic cells
Do not divide
regularly, variably
differentiated
Liver, Pancreas,
Salivary glands
V. Fixed postmitotic cells
Do not divide,
highly differentiated
Neurons, Striated
muscle cells
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Sensitivity
High
Low
Ahmed Group
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Lecture 7
Random nature of cell killing and Poisson statistics
Doses for inactivation of viruses, bacteria, and eukaryotic
cells after irradiation
Single hit, multi-target models of cell survival
Two component models
Linear quadratic model
Calculations of cell survival with dose
Effects of dose, dose rate, cell type
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Survival Models
A. Linear Hypothesis
B. Quadratic Hypothesis
C. Linear-Quadratic Hypothesis
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Two major types of cell survival curves
Exponential
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Sigmoid
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Survival Curves for Mammalian cells
The first dose-survival curve for mammalian cells was published in 1956.
Unlike earlier curves for bacteria and viruses, those for mammalian cells exhibit
an initial “quasi-shoulder” before becoming steeper and approximately semilogarithmic at higher doses. The progressively steeper survival curve reflects a
linear “single hit” exponential decline in cell survival upon which is
superimposed a second mechanism which becomes progressively more lethal
with increasing dose. This ”multi-hit”mechanism based on an accumulation of
sublethal lesions which are increasingly likely to interact to become lethal.
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Shape of the cell survival curve
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Single hit / multi-target
Shouldered Curve
Puck and Marcus 1956
S = 1- (1-e-D/D0)n
Where “n” is extrapolation number,
D0 is the slope
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Parameters of survival curves
PE:
Plating efficiency.
colonies
Dq:
The quasithreshold dose for a given population that
often measures the width of the shoulder
D0:
The dose that reduces the surviving fraction to 1/e
(=0.37) on the exponential portion of the curve or the
dose that produces 37% survival.
n:
Extrapolation number. This value is obtained by
extrapolating the exponential portion of the curve
to the abscissa.
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Percentage of cells able to form
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Target theory
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Linear Hypothesis
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Linear hypothesis is valid at low doses of X-rays (21-87
rads).
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At a dose of 21 rads, the split dose technique failed to
reveal any repair of sub-lethal damage
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Thus, the exponential curve after radiation is not a result
of single hit or a single sensitive target rather a sum of
several factors
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The shoulder region shows the extent of accumulation of
sublethal damage before cells lose reproductive integrity
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The shoulder region shows a repair process operate at the
outset of radiation, but becomes ineffective as the dose
increases until the processes of damage continue without
concomitant repair
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Quadratic Hypothesis
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The surviving fraction decreases as a function of the dose
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Linear-Quadratic Hypothesis
Survival curves show continuously increasing curvature,
following a linear portion. This reflects:
1. A component of cell kill proportional to dose (DSBs)
2. A component proportional to dose2 (SSBs).
S = e –(αd + βd²)
Where α and β are constants.
3. These two components may progress at different rate.
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The combined effect of non-repairable and repairable injury
can be quantified in terms of coefficients, α, for single-hit nonrepairable injury, expressed in units of Gy -1, and β for multievent interactive repairable injury, in units of Gy -2. At least over
a dose range of about 1.0-8.0 Gy, a sufficiently accurate
description of the dose survival curve is:
Surviving fraction (SF) = e –(αd + βd²)
From this equation and from the next slide it is apparent that
at low doses most cell killing results from “α-type” (single-hit,
non-repairable) injury, but that as the dose increases, the
“β –type” (multi-hit, repairable) injury becomes predominant,
increasing as the square of the dose.
Lecture 7
Ahmed Group
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Lecture 7
Random nature of cell killing and Poisson statistics
Doses for inactivation of viruses, bacteria, and eukaryotic
cells after irradiation
Single hit, multi-target models of cell survival
Two component models
Linear quadratic model
Calculations of cell survival with dose
Effects of dose, dose rate, cell type
Ahmed Group
Lecture 7
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Intrinsic Radiation Sensitivity and Cell
Survival Curves
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Lecture 7
The mean inactivation dose (D) is calculated for published in vitro
survival curves obtained from cell lines of both normal and
neoplastic human tissues.
Cells belonging to different histological categories (melanomas,
carcinomas, etc.) are shown to be characterized by distinct values of
D which are related to the clinical radiosensitivity of tumors from
these categories.
Compared to other ways of representing in vitro radiosensitivity,
e.g., by the multitarget parameters D0 and n, the parameter D has
several specific advantages: (i) D is representative for the whole cell
population rather than for a fraction of it; (ii) it minimizes the
fluctuations of the survival curves of a given cell line investigated by
different authors; (iii) there is low variability of D within each
histological category; (iv) significant differences in radiosensitivity
between the categories emerge when using D. D appears to be a
useful concept for specifying intrinsic radiosensitivity of human cell
lines.
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Linear-quadratic model
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Survival curve and multi-fraction
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Calculation of cell survival with dose
Problem 1: A tumor consists of 109 clonogenic cells. The effective response curve, given in daily fractions of
2 Gy, has no shoulder and a D0 of 3 Gy. What total dose is required to give a 90% chance of cure?
Answer:
To give a 90% probability of tumor control in a tumor containing 10 9 cells requires a cellular depopulation
of 10-10. The dose resulting in one decade of cell killing (D10 ) is given by D10 = 2.3 x D0 = 2.3 x 3 = 6.9 Gy
Therefore, total dose for 10 decades of killing = 6.9 x 10 = 69 Gy
Problem 2: Suppose that in the previous example, the clonogenic cells underwent three cell doublings during
treatment. What total dose would be required to achieve the same probability of tumor control?
Answer:
Three cell doublings would increase the cell number by 2 x 2 x 2 = 8. Consequently, about one extra decade of cell
killing would be required, corresponding to an additional dose of 6.9 Gy. Total dose is 69 + 6.9 = 75.9 Gy.
Problem 3: During the course of radiotherapy, a tumor containing 109 cells receives 40 Gy. if the Do is 2.2. Gy,
how many tumor cells will be left?
Answer:
If the Do is 2.2 Gy the D10 is: D10 = 2.3 x Do = 2.3 x 2.2 = 5 Gy. Because the total dose is 40 Gy, the number of
decades of cell killing is 40/5 = 8. Number of cells remaining = 10 9 x 10-8 = 10
Problem 4: If 107 cells were irradiated according to single-hit kinetics so that the average number of hits per
cell is one, how many cells would survive?
Answer:
A dose that gives an average of one hit per cell is the Do; that is, the dose that on the exponential region of the
survival curve reduces the number of survivors to 37%; the number of surviving cells therefore is:
107 x 37/100 = 3.7 x 106
Lecture 7
Ahmed Group
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Lecture 7
Random nature of cell killing and Poisson statistics
Doses for inactivation of viruses, bacteria, and eukaryotic
cells after irradiation
Single hit, multi-target models of cell survival
Two component models
Linear quadratic model
Calculations of cell survival with dose
Effects of dose, dose rate, cell type
Ahmed Group
Hyper-radiation sensitivity and induced
radiation resistance
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Two types of sub-structures in cell survival
curve
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Fractionation of
radiation dose
increases cell
survival
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Surviving fraction for cells irradiated
to 6 Gy
Treatment
Controls
0.3 Gy x 20 fractions
1 Gy x 6 fractions
2 Gy x 3 fractions
3 Gy x 2 fractions
6 Gy x 1 fractions
C3H cells
(plateau phase)
(0.37)
0.30
0.36
0.52
0.11
0.06
C3H cells
(Exponential)
(0.34)
0.24
0.33
0.55
0.20
0.10
V-79 cells
(plateau phase)
(0.59)
0.28
0.34
0.65
0.14
0.08
Smith et al, IJROBP1999
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The lower the
dose rate, the
higher the
survival
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Cell-survival curves for Chinese hamster cells at various
stages of the cell cycle
From Sinclair W.K., Radiat Res. 33:620-643, 1968. The broken line is
a calculated curve expected to apply to mitotic cells under hypoxia.
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Summary:
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The damage induced by radiation can cause cell death (apoptosis),
prolonged cell cycle arrest (dose = 0.1 to 10 Gy) or reproductive death-loss of
clonogenicity.
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Ionizations produced within cells by irradiation are distributed randomly.
Consequently, cell death follows random probability statistics, Poisson
statistics.
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Do is the mean lethal dose, or the dose that delivers one lethal event per
target.
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Mammalian cells are significantly more radiosensitive than microorganisms
due to differences in DNA content and more efficient repair system.
Sterilizing radiation dose for bacteria is 20,000 Gy.
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A cell survival curve is the relationship between the fraction of cells
retaining their reproductive integrity and absorbed dose.
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Conventionally, surviving fraction on a logarithmic scale is plotted on the
ordinate, the dose is on the abscissa. The shape of the survival curve is
important
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Summary:
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The cell-survival curve for densely ionizing radiations (α-particles and lowenergy neutrons) is a straight line on a log-linear plot, that is survival is an
exponential function of dose.
The cell-survival curve for sparsely ionizing radiations (X-rays, gamma-rays
has an initial slope, followed by a shoulder after which it tends to straighten
again at higher doses.
At low doses most cell killing results from “α-type” (single-hit, nonrepairable) injury, but that as the dose increases, the“β –type” (multi-hit,
repairable) injury becomes predominant, increasing as the square of the
dose.
Survival data are fitted by many models. Some of them are: linear
hypothesis, linear-quadratic hypothesis, quadratic hypothesis.
The survival curve for a multifraction regimen is an exponential function of
dose. The average value of the Do for the multifraction survival curve for
human cells is about 3 Gy.
The D10, the dose resulting in one decade of cell killing, is related to the Do by
the expression D10 = 2.3 x Do
Cell survival depends on the dose, dose rate and the cell type
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