scholarly journals Predictive Monitoring of Shake Flask Cultures with Online Estimated Growth Models

2021 ◽  
Vol 8 (11) ◽  
pp. 177
Author(s):  
Barbara Pretzner ◽  
Rüdiger W. Maschke ◽  
Claudia Haiderer ◽  
Gernot T. John ◽  
Christoph Herwig ◽  
...  

Simplicity renders shake flasks ideal for strain selection and substrate optimization in biotechnology. Uncertainty during initial experiments may, however, cause adverse growth conditions and mislead conclusions. Using growth models for online predictions of future biomass (BM) and the arrival of critical events like low dissolved oxygen (DO) levels or when to harvest is hence important to optimize protocols. Established knowledge that unfavorable metabolites of growing microorganisms interfere with the substrate suggests that growth dynamics and, as a consequence, the growth model parameters may vary in the course of an experiment. Predictive monitoring of shake flask cultures will therefore benefit from estimating growth model parameters in an online and adaptive manner. This paper evaluates a newly developed particle filter (PF) which is specifically tailored to the requirements of biotechnological shake flask experiments. By combining stationary accuracy with fast adaptation to change the proposed PF estimates time-varying growth model parameters from iteratively measured BM and DO sensor signals in an optimal manner. Such proposition of inferring time varying parameters of Gompertz and Logistic growth models is to our best knowledge novel and here for the first time assessed for predictive monitoring of Escherichia. coli (E. coli) shake flask experiments. Assessments that mimic real-time predictions of BM and DO levels under previously untested growth conditions demonstrate the efficacy of the approach. After allowing for an initialization phase where the PF learns appropriate model parameters, we obtain accurate predictions of future BM and DO levels and important temporal characteristics like when to harvest. Statically parameterized growth models that represent the dynamics of a specific setting will in general provide poor characterizations of the dynamics when we change strain or substrate. The proposed approach is thus an important innovation for scientists working on strain characterization and substrate optimization as providing accurate forecasts will improve reproducibility and efficiency in early-stage bioprocess development.

2020 ◽  
Vol 14 (1) ◽  
Author(s):  
Fernanda Carini ◽  
Alberto Cargnelutti-Filho ◽  
Jéssica Maronez De Souza ◽  
Rafael Vieira Pezzini ◽  
Cassiane Ubessi ◽  
...  

The objective of this study was to fit a logistic model to fresh and dry matters of leaves and fresh and dry matters of shoots of four lettuce cultivars to describe growth in summer. Cultivars Crocantela, Elisa, Rubinela, and Vera were evaluated in the summer of 2017 and 2018, in soil in protected environment and in soilless system. Seven days after transplantation, fresh and dry leaf matters and fresh and dry shoot matters of 8 plants were weighed every 4 days. The model parameters were estimated using the software R, using the least squares method and iterative process of Gauss-Newton. We also estimated the confidence intervals of the parameters, verified the assumptions of the models, calculated the goodness-of-fit measures and the critical points, and quantified the parametric and intrinsic nonlinearities. The logistic growth model fitted well to fresh and dry leaf and shoot matters of cultivars Crocantela, Elisa, Rubinela, and Vera and is indicated to describe the growth of lettuce.


2021 ◽  
Author(s):  
Matthew J Simpson ◽  
Alexander Browning ◽  
David James Warne ◽  
Oliver J Maclaren ◽  
Ruth E Baker

Sigmoid growth models, such as the logistic and Gompertz growth models, are widely used to study various population dynamics ranging from microscopic populations of cancer cells, to continental-scale human populations. Fundamental questions about model selection and precise parameter estimation are critical if these models are to be used to make useful inferences about underlying ecological mechanisms. However, the question of parameter identifiability for these models -- whether a data set contains sufficient information to give unique or sufficiently precise parameter estimates for the given model -- is often overlooked; We use a profile-likelihood approach to systematically explore practical parameter identifiability using data describing the re-growth of hard coral cover on a coral reef after some ecological disturbance. The relationship between parameter identifiability and checks of model misspecification is also explored. We work with three standard choices of sigmoid growth models, namely the logistic, Gompertz, and Richards' growth models; We find that the logistic growth model does not suffer identifiability issues for the type of data we consider whereas the Gompertz and Richards' models encounter practical non-identifiability issues, even with relatively-extensive data where we observe the full shape of the sigmoid growth curve. Identifiability issues with the Gompertz model lead us to consider a further model calibration exercise in which we fix the initial density to its observed value, neglecting its uncertainty. This is a common practice, but the results of this exercise suggest that parameter estimates and fundamental statistical assumptions are extremely sensitive under these conditions; Different sigmoid growth models are used within subdisciplines within the biology and ecology literature without necessarily considering whether parameters are identifiable or checking statistical assumptions underlying model family adequacy. Standard practices that do not consider parameter identifiability can lead to unreliable or imprecise parameter estimates and hence potentially misleading interpretations of the underlying mechanisms of interest. While tools in this work focus on three standard sigmoid growth models and one particular data set, our theoretical developments are applicable to any sigmoid growth model and any relevant data set. MATLAB implementations of all software available on GitHub.


2010 ◽  
Vol 53 (1) ◽  
pp. 101-107
Author(s):  
M. Mendeş

Abstract. The main objective of this study was to predict mono and multiphasic growth model parameters of broilers. For this purpose daily body weights-age data of 106 male and female chickens reared under different stocking densities (GR1=11 birds/m2 , GR2=17 birds/m2 and GR3=25 birds/m2) were used. Results of mono and multiphasic (diphasic and triphasic) growth curve analyses showed that defining the growth of birds using multiphasic growth models instead of monophasic growth models, displays more detailed and reliable results. Based on goodness-of-fit criteria, lead to the choice of a triphasic logistic growth function for GR1 and GR2, and diphasic function for GR3 males and females.


2021 ◽  
Vol 38 (2) ◽  
pp. 229-236
Author(s):  
Ayşe Van ◽  
Aysun Gümüş ◽  
Melek Özpiçak ◽  
Serdar Süer

By the study's coverage, 522 individuals of tentacled blenny (Parablennius tentacularis (Brünnich, 1768)), were caught with the bottom trawl operations (commercial fisheries and scientific field surveys) between May 2010 and March 2012 from the southeastern Black Sea. The size distribution range of the sample varied between 4.8-10.8 cm. The difference between sex length (K-S test, Z=3.729, P=0.000) and weight frequency distributions (K-S test, Z=3.605, P=0.000) was found to be statistically significant. The length-weight relationship models were defined as isometric with W = 0.009L3.034 in male individuals and positive allometric with W = 0.006L3.226 in female individuals. Otolith and vertebra samples were compared for the selection of the most accurate hard structure that can be used to determine the age. Otolith was chosen as the most suitable hard structure. The current data set was used to predict the best growth model. For this purpose, the growth parameters were estimated with the widely used von Bertalanffy, Gompertz and Logistic growth functions. Akaike's Information Criterion (AIC), Lmak./L∞ ratio, and R2 criteria were used to select the most accurate growth models established through these functions. Model averaged parameters were calculated with multi-model inference (MMI): L'∞ = 15.091 cm, S.E. (L'∞) = 3.966, K'= 0.232 year-1, S.E. (K') = 0.122.


Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. D145-D155
Author(s):  
Qingxin Meng ◽  
Xiangyun Hu ◽  
Heping Pan ◽  
Huolin Ma ◽  
Miao Luo

The application of the Cole-Cole model within time-domain induced polarization (TDIP) forward field modeling shows that the model parameters can characterize time-varying states of the TDIP field and support observed data analysis. The Cole-Cole model contains real and imaginary parts, and it requires a frequency-to-time conversion for TDIP forward modeling. However, the TDIP field is usually expressed by a real number, and its intuitive time-varying states field intensity increases with charging time. Therefore, the forward model should be constructed in a simpler form. We have aimed to develop a forward model using mathematical functions not based on physical principles. The Weibull (WB) growth model, which is primarily used to describe the time-varying curve features in regression analysis, is introduced into the basic algorithm of the TDIP forward model. Subsequently, a forward expression of the TDIP effect is established. Based on the time-varying shape and scale parameters, this expression describes the time-varying rate and relaxation states of the TDIP fields. Furthermore, based on the extensively used conjugate gradient optimization, an apparent WB parameter scheme is initiated to calculate the spectral parameters that represent the relaxation and time-varying rate obtained from the multi-time-channel TDIP data. Finally, this scheme is applied to interpret the different simulated and actual TDIP data. The results demonstrate that the WB growth model can be used for the TDIP forward model without involving physical principles, the model parameters without specific physical significance can be used to represent the time-varying states of TDIP fields, and apparent WB parameters can be used to discern different TDIP observed data. The setting of the TDIP forward model and model parameters can actually be more flexible and diverse, so as to obtain simpler forward expressions and ensure a highly efficient inverse solution.


2008 ◽  
Vol 158 (3) ◽  
pp. 287-294 ◽  
Author(s):  
Juergen Honegger ◽  
Sanna Zimmermann ◽  
Tsambika Psaras ◽  
Manfred Petrick ◽  
Michel Mittelbronn ◽  
...  

ObjectiveRecent observational studies have established progression and recurrence rates of pituitary adenomas. However, it is still unknown how individual pituitary adenomas grow over years and whether growth kinetics follow a distinct growth model. The objective of this study was to define a growth model for non-functioning pituitary adenomas.MethodsFifteen patients who had five or more serial high-quality examinations with magnetic resonance images or computerized tomography scans were identified among 216 patients with non-functioning pituitary adenomas. Tumour volumes were assessed using a stereological method based on the Cavalieri principle. Tumour growth during the observation period was analysed and different growth models were fitted to the data.ResultsFifteen pituitary adenomas (12 recurrent tumours and 3 newly diagnosed tumours) were longitudinally observed during a median observation period of 7.4 years (range: 2.3–11.9 years). Growth kinetics could be described either by an exponential growth model (nine patients) or by a logistic model (five patients) with initial exponential growth followed by deceleration of growth. One tumour remained unchanged in size during the observation period. None of the adenomas showed accelerated growth during the observation period. Overall, the linear growth model was not suitable to describe the growth kinetics of non-functioning pituitary adenomas.ConclusionsOur study shows that growth of pituitary adenomas can be described by distinct growth models. Knowledge of growth dynamics has implications for clinical practice and helps to adjust scanning protocols for follow-up investigations.


2011 ◽  
Vol 250-253 ◽  
pp. 2583-2587
Author(s):  
Yu Qi Li ◽  
Huan Zhang ◽  
Yi Ran Liu

Logistic model is modified through introducing the pseudo construction settlement. Based on the observed settlement data of foundation in Yangshan deepwater port project, Logistic growth model and modified Logistic growth model are used for nonlinear regression analysis of foundation settlement respectively. It is indicated that the fitting curves by using modified Logistic growth model agree better with the observed settlement values than those by using Logistic growth model and that the correlation coefficients by using modified Logistic growth model are also bigger. Model parameters of different geological conditions obtained by nonlinear regression analysis can be used for significant reference to foundation settlement prediction of similar geological condition in other deepwater port.


2016 ◽  
Vol 23 (2) ◽  
pp. 387-402 ◽  
Author(s):  
Isabel P. Albaladejo ◽  
María Pilar Martínez-García

The tourism area life cycle (TALC) model of Butler explains the temporal evolution of a tourism resort. Lundtorp and Wanhill find that the logistic growth model represents the first phases of the TALC model. However, since the logistic model assumes a fixed tourism market ceiling, it fails to explain the poststagnation stage, where rejuvenation, decline, or any other intermediate possibility may arise. Taking into account the data of passenger flows to Bornholm from 1912 to 2001 collected by Lundtorp and Wanhill, the authors find that the superposition of several logistic growth models fits better with these data. Then they propose a multilogistic growth model, where investment or innovation in the tourism sector boosts the addition of new logistic curves which superpose the old ones. The continuous birth and superposition of these new life cycles is not free; it requires the purposive effort of entrepreneurs and governments seeking new markets and the improvement of infrastructures.


2021 ◽  
Vol 13 (2) ◽  
pp. 465-485
Author(s):  
Agus Kartono ◽  
Setyanto Tri Wahyudi ◽  
Ardian Arif Setiawan ◽  
Irmansyah Sofian

The COVID-19 pandemic was impacting the health and economy around the world. All countries have taken measures to control the spread of the epidemic. Because it is not known when the epidemic will end in several countries, then the prediction of the COVID-19 pandemic is a very important challenge. This study has predicted the temporal evolution of the COVID-19 pandemic in several countries using the logistic growth model. This model has analyzed several countries to describe the epidemic situation of these countries. The time interval of the actual data used as a comparison with the prediction results of this model was starting in the firstly confirmed COVID-19 cases to December 2020. This study examined an approach to the complexity spread of the COVID-19 pandemic using the logistic growth model formed from an ordinary differential equation. This model described the time-dependent population growth rate characterized by the three parameters of the analytical solution. The non-linear least-squares method was used to estimate the three parameters. These parameters described the rate growth constant of infected cases and the total number of confirmed cases in the final phase of the epidemic. This model is applied to the spread of the COVID-19 pandemic in several countries. The prediction results show the spread dynamics of COVID-19 infected cases which are characterized by time-dependent dynamics. In this study, the proposed model provides estimates for the model parameters that are good for predicting the COVID-19 pandemic because they correspond to actual data for all analyzed countries. It is based on the coefficient of determination, R2, and the R2 value of more than 95% which is obtained from the non-linear curves for all analyzed countries. It shows that this model has the potential to contribute to better public health policy-making in the prevention of the COVID-19 pandemic.


1994 ◽  
Vol 51 (3) ◽  
pp. 516-526 ◽  
Author(s):  
W. M. Mooij ◽  
E. H. R. R. Lammens ◽  
W. L. T. Van Densen

The growth rate of young-of-the-year of the six most abundant fish species (smelt (Osmerus eperlanus), pikeperch (Stizostedion lucioperca), perch (Perca fluviatilis), ruffe (Gymnocephalus cernua), bream (Abramis brama), and roach (Rutilus rutilus)) in Lake Tjeukemeer was predicted from water temperature using the model [Formula: see text]. For each species the model parameters were estimated using data from approximately 120 field observations of body size over a period of 13 yr; about 94% of the variance in body size could be explained by the model. The growth rate was correlated with temperature for all planktivorous species, except smelt. The relationship between growth rate and temperature was also significant for piscivorous pikeperch but not for benthivorous ruffe. These conclusions were corroborated by comparing the unexplained sum of squares of the temperature growth model with that of a temperature-neutral, logistic growth model. The abundance of food was not related to the temperature-corrected growth rate of planktivorous fishes, except in one year during which food conditions were extremely poor. We concluded that in most years the growth rate of 0+ planktivorous fish was not food limited. For piscivorous pikeperch, however, the variation in growth rate could be explained by the higher availability of smelt in warmer years.


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