Details

Snapshot 1: survival and injury curves produced with the Weibullian model with shape factor

Snapshot 2: survival and injury curves produced with the log-linear, first-order kinetic model that corresponds to the Weibullian model with a shape factor

Snapshot 3: survival and injury curves produced with the Weibullian model with shape factor ("tailing")

Traditionally, the survival curves of microbial cells and bacterial spores exposed to a hostile environment or lethal agent (e.g. heat, ultra-high hydrostatic pressure, or chemical disinfectant) are determined by counting the survivors' colonies after incubation under optimal conditions with respect to temperature, pH, nutrients, and so on. Under such conditions, injured cells or spores are likely to be counted as survivors. If the recovery is made after incubation under stressful conditions, then it is likely that only intact cells or spores will produce colonies, and hence the difference is an indicator of the number or fraction of the injured cells. It is possible, however, to incubate the survivors under several levels of stress in order to reveal the numbers of intact survivors and those at various levels of injury. This has actually been done, albeit infrequently.

In this Demonstration, the principle is demonstrated by simulating regular survival curves accompanied by curves representing the intact, slightly injured, and gravely injured survivors. The curves, shown on linear and semilogarithmic coordinates, are generated with the Weibullian model , where is the survival ratio (that is, , where is the count after exposure time and is the initial number), is a characteristic time ("scale factor"), and is the shape factor. Where , the semilogarithmic curve has downward concavity, and where , it has upward concavity ("tailing"). The log-linear (first-order kinetics) model is a special case of the model where .

To create a set of four curves, select their Weibullian model's parameters (the and ), the time axis maximum, and the axis minimum with the sliders. The four curves will then be displayed, in different colors, on linear (top plot) and semilogarithmic (bottom plot) coordinates. By moving the time slider, the vertical gray line on the top plot will display the numerical values of the corresponding percentage of the cells or spores in each of the following states: intact, slightly injured, and gravely injured (green, blue, and purple, respectively), as well as the total momentary survival (red). The vertical gray line on the bottom plot displays the corresponding numerical values of their fraction expressed as its base-10 logarithm. The displayed numeric values above both plots are rounded to the first digit after the decimal point.

The objective of the Demonstration is only to demonstrate the principle of separating the degrees of injury. Hence, no attempt has been made to match the survival patterns of specific organisms or spores or to account for all possible separable injury levels.