Academic literature on the topic 'Modified Gompertz model'

The mathematical models can be used as a tool in predicting microbial population in sorghum fermentation, either spontaneous fermentation or fermentation with the addition of lactic acid bacteria (LAB) inoculum. Gompertz model modified by Gibson, Gompertz model modified by Zwietering, Baranyi-Robert model, Fujikawa model, Richards model, Schnute model were used in predicting the growth of lactic acid bacteria (LAB) and coliform bacteria during spontaneous fermentation, and also the growth of LAB during fermentation with the addition of inoculum. Meanwhile, there was death (inactivation) of coliform bacteria during sorghum fermentation with the addition of LAB inoculum. The Geeraerd model and the Gompertz model modified by Gil et al. were used to predict the inactivation. The accuracy and precision of models were evaluated based on the Root Mean of Sum Square Error (RMSE), coefficient of determination (R2), and curve fitting. Gompertz model modified by Gibson had the highest accuracy and precision, which was followed by the accuracy of the Fujikawa model and Baranyi-Robert model in predicting the growth of LAB and the growth of coliform bacteria during spontaneous fermentation. Meanwhile, in predicting LAB growth during fermentation with the addition of inoculum, high accuracy and precision was obtained from Richards and Schnute models. In predicting the inactivation of coliform bacteria, Geeraerd model provided higher accuracy and precision compared to Gompertz model modified by Gil et al. Keywords: fermentation; inoculum; mathematical; model; sorghum; spontaneous

The anaerobic degradation of gelatin results in a two-phase cumulative biogas production curve, i.e., diauxie behaviour. The modified Gompertz model is normally used to fit these curves but due to the diauxie it would result in a less accurate representation. Furthermore, this inhibition slows down the production of biogas in batch reactors. This study adapted the modified Gompertz model to fit cumulative biogas production curves with diauxie behaviour and to investigate the inhibition that leads to this diauxie. Results show that the two-phase Gompertz model can fit diauxie curves with high accuracy and that diauxie curves are not a direct consequence of the accumulation of volatile fatty acids produced in the process of anaerobic digestion.

Based upon the deterministic Gompertz law of cell growth, we have proposed a stochastic model of tumour cell growth, in which the size of the tumour cells is bounded. The model takes account of both cell fission (which is an ‘action at a distance’ effect) and mortality too. Accordingly, the density function of the size of the tumour cells obeys a functional Fokker–Planck Equation (FPE) associated with the bounded stochastic process. We apply the Lie-algebraic method to derive the exact analytical solution via an iterative approach. It is found that the density function exhibits an interesting kink-like structure generated by cell fission as time evolves.

ABSTRACT For prediction of the shelf life of the mushroom Agaricus bisporus, the growth curve of the main spoilage microorganisms was studied under isothermal conditions at 2 to 22°C with a modified Gompertz model. The effect of temperature on the growth parameters for the main spoilage microorganisms was quantified and modeled using the square root model. Pseudomonas spp. were the main microorganisms causing A. bisporus decay, and the modified Gompertz model was useful for modelling the growth curve of Pseudomonas spp. All the bias factors values of the model were close to 1. By combining the modified Gompertz model with the square root model, a prediction model to estimate the shelf life of A. bisporus as a function of storage temperature was developed. The model was validated for A. bisporus stored at 6, 12, and 18°C, and adequate agreement was found between the experimental and predicted data.

Abstract Because of the laboratory operating, the fineending of grain-size distribution (GSD) are simply combined as one point, which results in the information loss of the fine and very-fine clastic particles, and affects the geological parameters calculation of GSD. To remove the fine-endings, a modified Gompertz sigmoidal model is proposed in this paper. The first stage is establishing and solving the modified Gompertz sigmoidal model; the second stage is fitting and evaluating the cumulative probability and frequency of GSD; the third stage is calculating the geological parameters. Taking 113 samples for example, coefficients of determination (COD) between measured and fitted individual cumulative probability and frequency are bigger than 0.98980 and 0.97000 respectively, which proves the goodness of fitting results. By moments method using frequency data, the COD between fitted and measured mean is 0.97578, while CODs of sorting, skewness and kurtosis are in low values, which suggest that the fine-endings has little influence on the average grain-sizes of GSD and large influence on its geometry. Besides, modified Gompertz sigmoidal model offers another quick numerical way to calculate median, mean and sorting of GSD by graphical method using cumulative probability data. The proposed method is useful to remove the fine-endings and contribute to calculate the geological parameters of GDS.

The modified sigmoidal bacteria growth functions (the modified Gompertz, logistic, and Richards) were used to evaluate the methane production process kinetics of agricultural wastes. The mesophilic anaerobic co-digestion experiments were conducted with various agricultural wastes as feedstocks, including cow manure, corn straw, grape leaves, vines, wine residue, strawberry leaves, and tomato leaves. The results showed that anaerobic co-digestion of cow manure and other agricultural wastes increased the methane yields while it prolonged the lag phase time. Compared with the modified Gompertz and logistic models, the modified Richards model obtained higher correlation coefficients and was able to fit experimental data better. The results of this study were expected to determine a suitable model to simulate and study the kinetic process of anaerobic co-digestion with mixed agricultural wastes as feedstocks.

In this paper, we introduce a new continuous probability distribution with five parameters called the modified beta Gompertz distribution. It is derived from the modified beta generator proposed by Nadarajah, Teimouri and Shih (2014) and the Gompertz distribution. By investigating its mathematical and practical aspects, we prove that it is quite flexible and can be used effectively in modeling a wide variety of real phenomena. Among others, we provide useful expansions of crucial functions, quantile function, moments, incomplete moments, moment generating function, entropies and order statistics. We explore the estimation of the model parameters by the obtained maximum likelihood method. We also present a simulation study testing the validity of maximum likelihood estimators. Finally, we illustrate the flexibility of the distribution by the consideration of two real datasets.

The heat resistance of Listeria monocytogenes was determined in 0.1 M KH2PO4 buffer at three temperatures (50, 55, and 60°C), three pH levels (5, 6, and 7), and three NaCl concentrations (0, 2, and 4%). Survival curves were fit using nonlinear regression with a modified Gompertz equation. The Gompertz equation is capable of fitting survival curves which are linear, those which display an initial lag region followed by a linear region, and those which are sigmoidal. Parameter estimates were used to describe the lag region, death rate, and the tailing region of a survival curve. These estimates were also used to predict single and interactive effects of temperature, pH, and percentage of NaCl on the log surviving fraction (LSF) of bacteria. Interactions among these variables significantly (P < .05) affected the LSF. Generally, increased pH or NaCl concentration lead to an increased (P < .05) LSF, where as increased time or temperature lead to a decreased (P < .05) LSF. All multiple factor interactions significantly (P < .05) affected the LSF. These interactions differed depending on the heating medium and the region of the survival curve. The correlation of observed LSF and predicted LSF (R2 = .89) indicated that the Gompertz equation was in close agreement with the observations. This study demonstrated that the Gompertz equation and nonlinear regression can be used as an effective means to predict survival curve shape and response to heat of L. monocytogenes in many different environmental conditions.

It is shown that if the computer model of biological aging proposed by Stauffer is modified such that the late reproduction is privileged, then the Gompertz law of exponential increase of mortality can be retrieved.

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Livestock, especially cattle, has been considered one of the main sectors that is responsible for global warming due to rumen methane emission and, to a lesser extent, methane emission by residues. Another concern is the correct disposal of agroindustrial residues. The wet brewery grain is considered as polluting as animal wastes. Thus, such wastes must have correct destination, so their use to feed animal is an option. The wet brewery grain has been recorded as an important substitute for fodder and/or grain in ruminants diet. Thus, this study aimed at evaluating the potential for methane production in cattle fed diets containing different levels of wet brewery grain inclusion, to replace bulky diet, with 0, 20, 25 and 30% rates in dry matter percentage. Four castrated steers, with rumen cannula were studied and distributed in a Latin square design (4x4) in four experimental periods of 21 days each (14 days of adjustment and 7 days for data collection). During the last week of each period, the animals manure and ruminal fluid were collected, whose anaerobic digestion essays were analyzed, during the period of 120 days. So, the following parameters were evaluated: removal of total and volatile solids, removal of soluble chemical oxygen demand, cumulative and daily production of methane, volatile fatty acids production (lactic, acetic, propionic and butyric), acidity/alkalinity ratio and pH of reactors. In order to record ruminal fluid, 96-hour tests were performed in the laboratory to observe the influence of wet brewery grain inclusion on methane and volatile fatty acids production inside the rumen. The statistical evaluation of the process was obtained with curves of cumulative production of methane that were adjusted according to Gompertz modified model. Tukey test was used to compare averages with 5% significance. According to these data, it is concluded that wet brewery grain inclusion influenced on methane production for these animals. There was effect of treatment and period for cumulative production of methane (L). The treatment with the largest inclusion of wet brewery residue showed the highest potential of methane production in wastes. The wet brewery residue inclusion did not affect the production of volatile fatty acids inside rumen. The cumulative methane production (mL) of ruminal fluid was influenced by the inclusion of wet brewery residue on animals diet. Nevertheless, the lowest production occurred with an increasing supply of wet brewery residue. The Gompertz modified model provided a good adjustment to the methane production data. Consequently, wet brewery residue can be considered an alternative diet to replace corn silage up to 30% (DM), since it reduces methane production inside the rumen (environmental benefit) and increases methane production from residues (energy and economic benefit).
A pecuária, sobretudo a bovina, tem sido considerada um dos principais setores responsáveis pelo aquecimento global, devido à emissão de metano ruminal e, em menor proporção, à emissão de metano pelos dejetos. Outra preocupação é a correta destinação dos resíduos agroindustriais. O resíduo úmido de cervejaria é considerado tão poluidor quanto os dejetos animais. Desta forma, é importante que este subproduto tenha destino correto e uma opção é o uso na alimentação animal. O resíduo úmido de cervejaria tem se mostrado um importante substituto para forragens e/ou grãos na dieta de ruminantes. Portanto, o objetivo deste trabalho foi avaliar o potencial de produção de metano de bovinos alimentados com dietas que continham diferentes níveis de inclusão de resíduo úmido de cervejaria (RUC), em substituição ao volumoso da dieta, cujas doses foram: 0, 20, 25 e 30% em porcentagem de massa seca. Foram utilizados quatro bovinos machos, castrados, portadores de cânula ruminal, distribuídos em delineamento quadrado latino (4x4), em quatro períodos experimentais de 21 dias cada (14 dias de adaptação e 7 dias de coleta de dados). Na última semana de cada período, coletaram-se dejetos e líquido ruminal dos animais. Com os dejetos coletados, realizaram-se ensaios de biodigestão anaeróbia, no período de 120 dias, nos quais foram avaliados a remoção de sólidos totais e voláteis, a remoção da demanda química de oxigênio solúvel, a produção diária e acumulada de gás metano, a produção de ácidos graxos voláteis (lático, acético, propiônico e butírico), a relação acidez/alcalinidade e o pH dos reatores. Em relação ao líquido ruminal, foram realizados testes de 96 horas, em laboratório, para verificar a influência da inclusão de RUC na produção de gás metano e ácidos graxos voláteis no rúmen. Para a avaliação estatística do processo, utilizaram-se curvas de produção acumulada de metano, ajustadas segundo modelo de Gompertz modificado. O teste de Tukey foi adotado para comparação das médias, com nível de significância de 5%. Com os dados obtidos, conclui-se que a inclusão de resíduo úmido de cervejaria teve influência na produção de metano nesses animais; houve efeito de tratamento e período para a produção acumulada de metano (L). O tratamento com maior inclusão de resíduo úmido de cervejaria apresentou maior potencial de produção de metano nos dejetos; a inclusão de RUC não alterou o perfil de produção de ácidos graxos voláteis no rúmen; a produção acumulada de metano (mL) do líquido ruminal foi influenciada pela inclusão de resíduo úmido de cervejaria à dieta. Todavia, a menor produção ocorreu com o aumento do fornecimento de resíduo úmido de cervejaria. O modelo de Gompertz modificado apresentou bom ajuste aos dados de produção de gás metano. Logo, o resíduo úmido de cervejaria pode ser considerado alimento alternativo para substituir a silagem de milho, em até 30% (MS), uma vez que diminui a produção de metano no rúmen (benefício ambiental) e aumenta a produção de metano nos dejetos (benefício energético e econômico).

Pecan nuts might become contaminated with foodborne pathogens, such as Salmonella and E. coli., through birds and other potential sources of contamination that can lead to serious illness or even death, as well as financial losses. For example, the outbreak of Salmonella in pecan products in Texas caused major product recalls in 2010. Irradiation with electron beams could be an effective method of preventing potential outbreaks without changing the pecans' taste, color and flavor and without causing any risk of recontamination before the product reaches the consumer. However, when irradiation is applied alone, the shelf life of the product is decelerated because of the detrimental effect of lipid oxidation. Therefore, to extend the shelf of the pecans while assuring their safety, irradiation of pecans under modified atmosphere packing (MAP) conditions could be a viable option. This research showed that when treated with electron beams, surrogates of Escherichia coli (a cocktail of BAA-1427, BAA-1428, and BAA-1430), and Salmonella (S. Typhimurium LT2) were more resistant to ionizing radiation (higher D10 values) when packed under vacuum (VP) than under air or other MAP conditions. This research also showed that lipid oxidation in pecans (due to exposure to ionizing radiation) shows a lag phase, probably due to the antioxidants present in pecan nuts. The lag phase represents a delay period before the pecan nuts start to get rancid (increase in PV formation), and it is best described by a modified Gompertz model. Kinetic evaluation of the lipid oxidation reaction suggests that the dose level has a more drastic effect in PV formation than the type of package used during the irradiation treatment, e.g., vacuum packed versus nitrogen-packed. Moreover, accelerated shelf life studies (4 weeks at 48.9oC) showed that vacuum-packed (VP) pecans can be stored at -25 degrees C up to three years, while irradiated (at 3.0 kGy) VP pecans can be stored only for eight months, without the detrimental effects of lipid oxidation. Therefore, irradiation of pecans under air at 3.0 kGy reduces the shelf life of the nuts in terms of rancidity, but vacuum-packaging can be used to extend their shelf-life. Irradiation in oxygen packaging increases rancidity and the oxidation reaction rate accelerates with increasing dose. Irradiation under nitrogen packaging requires lower doses to achieve the almost same number of log reductions in microbial population. The use of nitrogen packaging also inhibits the oxidative reaction leading to rancidity in pecans. Although there are some drawbacks to the application of nitrogen packaging in an irradiation plant (special machinery and packaging films (permeability specifications for N2 gas)), the savings induced by avoiding recalls may make this technology worthy of consideration.

Abstract Biogas production is an anaerobic waste-to-energy technology, involving waste degradation and stabilization. The sustainable, cheap and clean nature of biogas has led to the unprecedented rise in its use as an alternative energy source. Due to the increased interests, availability of conventional biodegradable organics has shrunk enormously over the years, necessitating the aggressive search for novel energy crops and substrate enhancement options. These novel options ensure feedstock security, optimize conventional biomass feedstocks, improve feedstock degradability and increase in biogas yield. Low biodegradability of most lignocellulosic wastes like okra waste, limits their use as a viable substrate in the anaerobic digestion process. Over the years, several elements, compounds and nanoparticles have been applied to anaerobic digestion systems as supplementary nutrients with a view to enhancing substrate degradation. Such supplements like iron-based additives have gained prominence in anaerobic digestion processes of wastes, owing to their electron donation abilities, promotion of solubilization, hydrolysis, acidification, and hydrogenotrophic methanogenesis. In a bid to enhance substrate degradation, reduce inhibitions, increase both biogas yield and methane content, a comparative study on the influence of four different iron-based additives (nanoscale zero-valent iron (nZVI), Polypyrrole-magnetic nanocomposite (Ppy-Fe3O4), Iron powder (Fe) and Hematite (Fe2O3)) on the entire anaerobic digestion of okra waste was done. Previously determined optimum doses, 20 mg, 20 mg, 750 mg, 750 mg and 0 respectively for nZVI, Ppy-Fe3O4, Fe, Fe2O3 and control were added to the bioreactors containing okra wastes in a 500 mL biomethane potential bioreactors under mesophilic temperature (37°C) for 20 days. The cumulative volumes of the biogas from different reactors were recorded and analyzed. The morphological deformation, structures and analysis of the undigested substrate, digestates of substrate supplemented with iron-based additives and the control were evaluated with scanning electron microscopy (SEM). Artificial neural network (ANN) model and the modified Gompertz model were validated with the experimental data. The ANN model showed better goodness of fit and was better correlated with the experimental data. Experimental data were subjected to analysis of variance at a 95% confidence level. Results showed that Ppy-Fe3O4 additives better enhanced both biogas yield and methane contents significantly when compared to the control. It was also observed that all iron-additive supplemented processes were more degraded when compared with the control.