Wolfram Demonstrations Project

This Demonstration simulates and plots static sigmoid survival curves for microbial cells or spores subjected to heat treatment or exposed to a lethal agent such as a chemical preservative or disinfectant, ultra-high hydrostatic pressure, radiation, etc. The generated survival curve is plotted in semilogarithmic (top) and linear (bottom) coordinates. The curve can be of type I, where the initial upper concavity, when plotted on semilogarithmic coordinates, progressively changes to downward concavity, or type II, where the initial downward concavity progressively changes to upper concavity (tailing).

Contributed by: Mark D. Normand and Micha Peleg

Slider Zoom
Gamepad Controls
Automatic Animation

Snapshot 1: sigmoid survival curve of type I with an inconspicuous shoulder and low resistance

Snapshot 2: sigmoid survival curve of type I with a prominent shoulder and high resistance

Snapshot 3: sigmoid survival curve of type II with an inconspicuous shoulder and high residual survival

Snapshot 4: sigmoid survival curve of type II with a prominent shoulder and low residual survival

This Demonstration simulates and plots static sigmoid survival curves of microbial cells or spores of the kind occasionally recorded in thermal sterilization or pasteurization and also in nonthermal preservation treatments such as with a chemical preservative, natural antimicrobial, application of ultra-high hydrostatic pressure, exposure to radiation, etc.

Sigmoid microbial survival curves can be of two types [1]: type I, where the curve's initial upper concavity, when plotted on semilogarithmic coordinates, progressively changes to downward concavity, and type II, where the initial downward concavity, when plotted on semilogarithmic coordinates, progressively changes to upper concavity. In this Demonstration, type I survival is described by the model

, where

is the survival ratio (the momentary number of survivors

divided by the initial number

) and

, and

are coefficients entered with sliders. Type II survival is described by the model

, where again

is the survival ratio and

, and

are coefficients entered with sliders.

The generated survival curve for the chosen model and entered parameters is plotted on semilogarithmic (top display) and linear (bottom display) coordinates with the respective model's equation. The upper limit of the time axis, and in the case of the semilogarithmic plot, the lower limit of the

axis, can be varied using the sliders.

Notice that the model generating type I curves allows for the existence of a treatment time, marked by a vertical dashed line, beyond which no survivors will ever be found [2]. By setting either

to zero, the model can also be used to generate curves with unchanging downward or upward concavity, respectively.

The model generating type II curves allows for the existence of an asymptotic survival ratio ("extreme tailing") which is marked by a horizontal dashed line.

References

[1] M. Peleg, "Calculation of the Non-Isothermal Inactivation Patterns of Microbes Having Sigmoidal Isothermal Semi-logarithmic Survival Curves," Critical Reviews in Food Science and Nutrition, 43(6), 2003 pp. 645–658. doi:10.1080/10408690390251156.

[2] M. Peleg, Advanced Quantitative Microbiology for Food and Biosystems: Models for Predicting Growth and Inactivation, Boca Raton, FL: CRC Press, 2006.