Models of Cell Survival

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

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

Modes of Radiation Injury Primarily by ionization and free radicals Low LET (X- and gamma-rays) damage by free radicals 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

Resultant mode of inactivation There is no assay to differentiate the damage caused by radiation-induced ionization or free-radicals 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 The damage can cause cell death, prolonged cell cycle arrest or reproductive death.

Fate of Irradiated Cells Division Delay - (Dose = 0.1 to 10 Gy) Interphase Death - Apoptosis Reproductive Failure - Loss of clonogenicity

Quantitation of cell killing and Poisson statistics 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.

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

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

Chromosomal DNA is the principal target for radiation-induced lethality

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.

Chromosomal aberrations and cell survival

Survival curves for cell lines of human and rodent origin B

Radiation sensitivity profiles for cells of human origin

Categories of Mammalian Cell Radiosensitivity Cell Type Properties Examples Sensitivity I. Vegetative Divide regularly, Erythroblasts, High intermitotic cells no differentiation Intestinal crypt cells, Basal cells of oral mucous membrane II. Differentiating Divide regularly, Spermatocytes, Oocytes, intermitotic cells some differentiation Inner enamel of between division developing teeth III. Connective Tissue Divide irregularly Endothelial cells, Fibroblasts IV. Reverting post- Do not divide Liver, Pancreas, mitotic cells regularly, variably Salivary glands differentiated V. Fixed post- Do not divide, Neurons, Striated mitotic cells highly differentiated muscle cells Low

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

Survival Models Linear Hypothesis Quadratic Hypothesis Linear-Quadratic Hypothesis

Two major types of cell survival curves Exponential Sigmoid

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 semi-logarithmic 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.

Shape of the cell survival curve

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

Parameters of survival curves PE: Plating efficiency. Percentage of cells able to form 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.

Target theory

Linear Hypothesis Linear hypothesis is valid at low doses of X-rays (21-87 rads). At a dose of 21 rads, the split dose technique failed to reveal any repair of sub-lethal damage Thus, the exponential curve after radiation is not a result of single hit or a single sensitive target rather a sum of several factors The shoulder region shows the extent of accumulation of sublethal damage before cells lose reproductive integrity 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

Quadratic Hypothesis The surviving fraction decreases as a function of the dose

Linear-Quadratic Hypothesis Survival curves show continuously increasing curvature, following a linear portion. This reflects: A component of cell kill proportional to dose (DSBs) 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.

Surviving fraction (SF) = e –(αd + βd²) The combined effect of non-repairable and repairable injury can be quantified in terms of coefficients, α, for single-hit non- repairable injury, expressed in units of Gy -1, and β for multi- event 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.

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

Intrinsic Radiation Sensitivity and Cell Survival Curves 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.

Linear-quadratic model

Survival curve and multi-fraction

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 109 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 = 109 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

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

Hyper-radiation sensitivity and induced radiation resistance

Two types of sub-structures in cell survival curve

Fractionation of radiation dose increases cell survival

Surviving fraction for cells irradiated to 6 Gy C3H cells C3H cells V-79 cells (plateau phase) (Exponential) (plateau phase) Treatment Controls (0.37) (0.34) (0.59) 0.3 Gy x 20 fractions 0.30 0.24 0.28 1 Gy x 6 fractions 0.36 0.33 0.34 2 Gy x 3 fractions 0.52 0.55 0.65 3 Gy x 2 fractions 0.11 0.20 0.14 6 Gy x 1 fractions 0.06 0.10 0.08 Smith et al, IJROBP1999

The lower the dose rate, the higher the survival

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.

Summary: 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. Ionizations produced within cells by irradiation are distributed randomly. Consequently, cell death follows random probability statistics, Poisson statistics. Do is the mean lethal dose, or the dose that delivers one lethal event per target. 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. A cell survival curve is the relationship between the fraction of cells retaining their reproductive integrity and absorbed dose. 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

Summary: The cell-survival curve for densely ionizing radiations (α-particles and low-energy 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, 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. 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