Survival curve shapes

Barendsen, G.W. 1990. Mechanisms of cell reproductive death and shapes of radiation dose-survival curves of mammalian cells. Inter. Jour. Radiation Biol. 57 885-896. 

Figures presented in various sections apply to experiments in which pure cultures have been irradiated in a controlled medium. In actual practice one is faced with the problem of producing an arbitrarily defined level of commercial sterility in an undefined medium with a mixed population. Commercial sterility can mean anywhere from 10 8 to 10 ia organism/g. depending on the product and type of contamination. Systematic data which would give the detailed shape of the survival curve in the region of commercial interests are nonexistent. The results of a number of experiments in which workers claimed to have achieved sterility are tabulated in Table VII. In nearly all cases insufficient data were obtained to allow a satisfactory statistical evaluation. Furthermore, differences and confusion in the dosimetry make the data rather approximate.

Survival curves of some microorganisms exposed to PEEs have a characteristic sigmoidal shape when plotted in linear coordinates. Peleg (1995) described this phenomenon by the following model ... 

The determinants of sterility assurance that must be considered in determining appropriate treatment levels to achieve particular SALs (in this text it will be assumed that the target SAL is lO ) or in validating existing treatment levels are, therefore, bioburden (microorganisms contaminating the item prior to treatment) and the shape and slope of the survival curve. 

Beside bioburden, the other determinant of sterility assurance is the survival curve and its shape and its slope. It is not correct to assume that all survival curves are of the simple linear type when data is plotted on semilogarithmic graph paper. Three general types of survival curve have been reported, the exponential curve, the shouldered" curve, and the "tailed" curve (Fig. 4). 

These points also explain the semantic differences between a modifier or potentiator of radiation damage (by whatever mechanism) and a sensitizer (implying oxygen-mimetic or electron-accepting mechanisms) although the literature is not always consistent on this point. The radiation potentiation of platinum amine complexes in vitro is remarkably, and somewhat frustratingly, dependent on experimental conditions such as the time of incubation before irradiation and the phase of the cell cycle used occasional protection has even been seen by most workers. Consideration of these factors requires careful analysis of the shape and slope of the survival curves and is beyond the scope of this summary, but the factors need to be known for a complete description of the potentiating effect. 

The shape of the survival curves differs considerably. Whereas for photon irradiation the typically shouldered shape is observed, low energy carbon irradiation leads to an approximately linear dose response curve. 

Due to the different shape, the survival curves cannot be simply transformed Into each other by a common scaling factor applied to the dose values. Since the dose-response curve for low energy carbon Irradiation can be described by a linear term ... 

Since the physical characteristics are exactly the same for all three cases, the differences of predicted RBE values can be entirely attributed to the different reference low-LET survival curves which are used as input for the calculation (they are shown as insert in Fig. 29). Obviously the RBE is correlated with the shoulder shape of the photon dose response curve for pronounced shoulders, significantly enhanced RBE values are predicted, whereas with decreasing shoulder width, decreasing RBE values are expected, and in the extreme case RBE should be close to one for cell systems showing purely exponential survival curves for photon radiation [141]. 

Q10 (temperature coefficient) The increase in the rate of a chemical process due to raising the temperature by 10 C. quantal responses Are all-or-none responses, or qualitative responses, e.g. death or survival (in contrast to quantitative responses which are continuous variables). The underlying distribution is the binomial distribution. Log dose-response lines for quantal responses are frequently sigmoidal in shape, and since this is the same form as the integrated frequency distribution curve, the slope of the... 

Under nonvolatile market conditions, the shape of the survival probability and the resulting credit curve will take a different form to the shape implied in volatile market conditions the graphs may change to reflect the higher perceived likelihood of default. For example, the shape of the survival probability may take the form as shown in Exhibit 21.19. 

As can be seen in Eq. (9.23) the survival probability of a component is completely determined by its failure rate )t(t). Its general shape is known as the bathtub curve , which is similar to the curve of human mortality. The bathtub curve is shown in Fig. 9.12. 

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