Death rate curve

Fig. 1 Microbial death rate curves that illustrate concept of decimal reduction (D values) and probability of survivors. (From Ref. l)...

Fig. 1 Death rate curves illustrating decimal reduction concept. (From Ref l)...

Typical microbial survivors found can be classified into four general types as shown in Figure 4.2 (Moats, 1971). Curve A represents a typical survivor curve with a logarithmic death rate. Curve B is a type commonly found and shows an initial lag in death rate followed by a logarithmic death rate. Curve C is similar to curve A,... 

From equations (18) and (19) we find or = 191 days in case the two highest points mentioned above are omitted (S = 222 days in case they are included). Comparing the value 191 days with the value a = 161 days based on the Gompertz death-rate curve (670-day life span) and the value = 258 days inferred from Dr. Fiokers data, we see that the theoretical curve fits the experimental values about as well as would be expected from the Gompertz curve, and somewhat better than would have been expected on the basis of Dr. Finkel s acceptance region. 

The death rate coefficient is usually relatively small unless inhibitoiy substances accumulate, so Eq. (24-10) shows an exponential rise until S becomes depleted to reduce [L. This explains the usual growth curve (Fig. 24-21) with its lag phase, logarithmic phase, resting phase, and declining phase as the effect of takes over. 

Complete reports of the experiments mentioned in this affidavit were prepared by Dr. Schuler and Dr. Ellenbeck. In the case of the Schuler [Dingl experiments, I, personally, had to handle the reports. These reports consisted of the minute details of every single case of each patient experimented upon. In fact, the reports were complete with detailed charts, indicating the fever curves, the death rates, the complications, and so on. The list for distribution included "I.G. Farben Hoechst Behring Works."... 

Following the stationary phase the rate of cell death exceeds that of cell growth, and the cell number begins to decrease, resulting in the final death rate part of the curve. 

In an earlier section we saw two different patterns for two sets of survival curves. In Figure 13.2 a) the survival curves move further and further apart as time moves on. This pattern is consistent with one of the hazard rates (think in terms of death rates) being consistently above the other hazard rate. This in turn corresponds to a fairly constant hazard ratio, the situation we discussed in Section 13.4.1. So a constant hazard ratio manifests itself as a continuing separation in the two survival curves as in Figure 13.2 a). Note that the higher hazard rate (more deaths) gives the lower of the two survival curves. 

Data obtained by the survivor-curve method are plotted semilogarithmi-cally. Data points are connected by least-squares analysis. In most cases the equation used is the first-order death rate equation,... 

Han, Y. W. Death rates of bacterial spores Nonlinear survivor curves. Can J Microbio 21 1464-1467 (1975). 

More serious is the evident fact that Dr. Finkel applies the same acceptance region indiscriminately to the three very different sets of experimental data represented by her curves A, B, and C. It seems likely that the test was designed to handle the life-shortening data (curve A), because a <-test would not be inappropriate to life-span data, since the death-rate function g(t) is (rather crudely) Gaussian. A statistical analysis of the cmTe-C data would be difficult, because the experimental statistic t (20 per cent incidence time) is cumbersome to handle mathematically, as is evident in our discussion. But it is easy to show that Dr. Finkel s acceptance region is entirely inapplicable to the curve-B data ( proportion of animals that survived the latent period of 150 days and then died with osteogenic sarcomas ). 

A plot of In 5 against t is then a straight line, with negative slope equal to a. An example, from Burch (2), is shown in Fig. 1, and another example, from Cameron and Pauling (3), in Fig. 2. Sometimes, as has been pointed out in a recent discussion (4), resolution of the survival curve into the sum of two or more Hardin Jones exponentials, with death rates Oi and coefficients can be made ... 

Figure 5.24. Various hypotheses for microbial death rate strictly exponential form, curve I sudden death after a certain time of exposure, curve IV or curves II and III due to inequalities among cells in a population (Hinshelwood, The Chem. Kinetics of the Bacteria Cell, 1946, Oxford University Press.)...

These same kinetic methods of thermal death rates can also be applied to predict the time for detecting a flavor change in a food product. Dietrich et al. (Dl) determined a curve for the number of days to detect a flavor change of frozen spinach versus temperature of storage, i he data followed Eq. (9.12-8) and a first-order kinetic relation. 

Inspection of the death curves obtained from viable count data had early ehcited the idea that because there was usually an approximate, and under some circumstances a quite excellent, linear relationship between the logarithm of the number of survivors and time, then the disinfection process was comparable to a unimolecular reaction. This imphed that the rate of killing was a function of the amount of one of the participants in the reaction only, i.e. in the case of the disinfection process the number of viable cells. From this observation there followed the notion that the principles of first-order... 

The more usual pattern found experimentally is that shown by B, which is called a sigmoid curve. Here the graph is indicative of a slow initial rate of kill, followed by a faster, approximately linear rate of kill where there is some adherence to first-order reaction kinetics this is followed again by a slower rate of kill. This behaviour is compatible with the idea of a population of bacteria which contains a portion of susceptible members which die quite rapidly, an aliquot of average resistance, and a residue of more resistant members which die at a slower rate. When high concentrations of disinfectant are used, i.e. when the rate of death is rapid, a curve ofthe type shown by C is obtained here the bacteria are dying more quickly than predicted by first-order kinetics and the rate constant diminishes in value continuously during the disinfection process. 

Radiation is carcinogenic. The frequency of death from cancer of the thyroid, breast, lung, esophagus, stomach, and bladder was higher in Japanese survivors of the atomic bomb than in nonexposed individuals, and carcinogenesis seems to be the primary latent effect of ionizing radiation. The minimal latent period of most cancers was <15 years and depended on an individual s age at exposure and site of cancer. The relation of radiation-induced cancers to low doses and the shape of the dose-response curve (linear or nonlinear), the existence of a threshold, and the influence of dose rate and exposure period have to be determined (Hobbs and McClellan 1986). 

The hazard rate can be estimated from data by looking at the patterns of deaths (events) over time. This estimation process takes account of the censored values in ways similar to the way such observations were used in the Kaplan—Meier curves. 

Tire means by which chemicals enter the body are inhalation (breadiing), ingestion (swallowing), and absorption (skin or living tissue contact). Once in the system these chemicals may produce such symptoms as tissue irritation, rash, dizziness, anxiety, narcosis, headaches, pain, fever, tremors, shortness of breath, birth defects, paralysis, cancer, and death, to mention a few. The amount of chemical diat enters the body is called the "dose." The relationship that defines the body response to the dose given is called the "dose-response curve." The lowest dose causing a detectable response is the "threshold limit." The "limit" is dependent on factors such as particle size of contaminant, solubility, breathing rate, residence time in the system, and human susceptibility. 

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