Biomedical subjects

Mark D Normand

Publications and source records attributed to Mark D Normand.

4 recordsLinked to original sources

PubMed2006

An expanded Fermi solution for microbial risk assessment.

'Fermi solution' refers to an estimate of a quantity of interest derived from a sequence of guesses about factors of which detailed knowledge is unavailable. When one makes such guesses, it is unlikely that the large majority of them will be either too high or too low. Most probably, some of the overestimates will be offset by some of the underestimates, and the final result will be often close to the correct value. The method has been popularized as recreational physics but it has also been applied in risk assessment, where the factors involved, but not their exact magnitudes, are known. The concept has potential application in certain types of food poisoning risk assessments, and in estimating the number victims of a bioterrorist attack on the food or water supply, where some guessing is inevitable because of the absence of accurate relevant data. We consider a version of the method in which ranges instead of single values are entered as the factors' estimates. For simplicity, the risk to be assessed is taken to be the product of the factors, and their true values are regarded as being uniformly distributed over their respective ranges. The risk itself is therefore construed as a random variable with a probability distribution whose parameters are explicitly determined by the individual factors' ranges and which can often be approximated by a lognormal distribution. The mode of this lognormal distribution is taken to be the "best guess" of the risk, and a credible interval is constructed with a specified level of "confidence". The best guess and credible interval are shown to be robust against small perturbations of the ranges. Thus, even if the ranges are misspecified to some degree, assessments based on the best guess or credible interval will not be substantially altered. This can help to achieve consensus among assessors in situations where very little hard knowledge exists. The calculation procedure has been automated in software that has been made freely available over the Internet. The concept is demonstrated with two hypothetical problems: predicting the number of persons who would come down with acute food poisoning after consuming a contaminated dish, and estimating the number of daily salmonellosis cases in a large metropolitan area.

Confidence Intervals↗

PubMed2005

Modeling and predicting non-isothermal microbial growth using general purpose software.

Published experimental isothermal growth curves of Clostridium perfringens cells in ground ham were fitted with a modified three-parameter version of the logistic equation as a primary model and the temperature dependence of the three parameters by ad hoc empirical secondary models. These were used to predict the organism's non-isothermal growth curves under three different cooling regimes. The assumption has been that the organism's instantaneous (or momentary) non-isothermal growth rate is the isothermal rate at the given temperature at a time that corresponds to its instantaneous population size. This could be translated into a differential rate model equation, whose coefficients are constructed from terms that reflect the changing growth parameters with temperature and hence with time. The continuous rate equation, however, can be solved incrementally by a numerical procedure that can be implemented in similar purpose software like Microsoft Excel(R). In all three cases, there was good agreement between the growth curves predicted by the model and those found experimentally. This demonstrated that the procedure can be used to generate growth curves under complicated thermal histories that may include regular and irregular temperature oscillations.

Animals↗

PubMed2004

Calculating microbial survival parameters and predicting survival curves from non-isothermal inactivation data.

Irrespective of whether the isothermal semi-logarithmic survival curves of heat inactivated microbial cells or spores are linear or nonlinear, it is theoretically possible to numerically calculate their survival parameters from inactivation data obtained under non-isothermal conditions. A method to do the calculation, when the temperature history ('profile') is expressed algebraically, is demonstrated with simulated survival curves. It has been tested with the published survival data of Salmonella, whose nonlinear semi-logarithmic isothermal survival curves can be described by a power law model. The reported survival ratios of Salmonella, determined during non-isothermal heat treatments in a broth and in ground chicken breast, were used to estimate its isothermal survival parameters in the two media and their temperature dependence. These, in turn, were used to predict the cells' survival curves under different temperature 'profiles.' There was a good agreement between the predicted and the reported experimental survival curves in the broth case and reasonable agreement in the ground chicken breasts, where the database was considerably smaller The development of a mathematical method to calculate survival parameters from non-isothermal inactivation data will eliminate the need to determine these parameters under isothermal conditions, which can only be approximated and are technically difficult to perform. In many cases, the proposed method will also enable the determination of the survival parameters in the actual food or medium of interest, which may contain particles, or is too viscous to be heated and cooled effectively using the currently available experimental procedures. In principle, the described mathematical method can also be used to assess organisms' survival parameters in nonthermal inactivation processes, such as exposure to a dissipating chemical agent or the application of ultra high-pressure.

Animals↗

PubMed2003

Estimating microbial inactivation parameters from survival curves obtained under varying conditions--the linear case.

When the isothermal semi-logarithmic survival curves of heat inactivated microbial cells or spores are known to be linear it is possible to calculate their survival parameters from curves obtained under nonisothermal conditions, provided that the temperature history ('profile') satisfies certain simple mathematical requirements. These requirements have been identified. The concept was tested by retrieving the survival parameters of a Listeria-like organism from generated survival curves for linear and nonlinear heating profiles on which noise had been superimposed. The availability of such a procedure eliminates the need to determine the survival parameters under perfect isothermal conditions, which are difficult to create for technical reasons. It will also enable determination of the survival parameters in the actual medium of interest, which may contain particles or may be too viscous to be treated in a capillary or narrow tube as is currently done. The method can also be used to assess survival parameters in nonthermal inactivation. A treatment with a dissipating chemical agent or anti-microbial is an example. In principle, the concept can be extended to the more general situation where the isothermal or iso-concentration semi-logarithmic survival curves are clearly nonlinear, but this will require a modification of the model and a different numerical calculation procedure.

Computer Simulation↗