scholarly journals Dynamic Modeling of the Impact of Temperature Changes on CO2 Production during Milk Fermentation in Batch Bioreactors

Foods ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 1809
Author(s):  
Jožef Ritonja ◽  
Andreja Goršek ◽  
Darja Pečar ◽  
Tatjana Petek ◽  
Boštjan Polajžer
Keyword(s):  
Mathematical Model ◽  
Fermentation Process ◽  
Model Parameters ◽  
Temperature Changes ◽  
Simulation And Optimization ◽  
Design And Synthesis ◽  
Batch Bioreactor ◽  
Milk Fermentation ◽  
Batch Bioreactors ◽  
The Impact

Knowledge of the mathematical models of the fermentation processes is indispensable for their simulation and optimization and for the design and synthesis of the applicable control systems. The paper focuses on determining a dynamic mathematical model of the milk fermentation process taking place in a batch bioreactor. Models in the literature describe milk fermentation in batch bioreactors as an autonomous system. They do not enable the analysis of the effect of temperature changes on the metabolism during fermentation. In the presented extensive multidisciplinary study, we have developed a new mathematical model that considers the impact of temperature changes on the dynamics of the CO2 produced during fermentation in the batch bioreactor. Based on laboratory tests and theoretical analysis, the appropriate structure of the temperature-considered dynamic model was first determined. Next, the model parameters of the fermentation process in the laboratory bioreactor were identified by means of particle swarm optimization. Finally, the experiments with the laboratory batch bioreactor were compared with the simulations to verify the derived mathematical model. The developed model proved to be very suitable for simulations, and, above all, it enables the design and synthesis of a control system for batch bioreactors.

scholarly journals Control of Milk Fermentation in Batch Bioreactor

2020 ◽  
Vol 26 (1) ◽  
pp. 4-9 ◽  
Author(s):  
Jozef Ritonja ◽  
Andreja Gorsek ◽  
Darja Pecar
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Input Output ◽  
Chemical Substances ◽  
Heating And Cooling ◽  
Batch Bioreactor ◽  
Milk Fermentation ◽  
Main Disadvantage ◽  
Batch Bioreactors ◽  
And Control

In this paper, modelling and control of a batch bioreactor is studied. A main disadvantage of batch bioreactors compared to other types of bioreactors is their inability to introduce biological or/and chemical substances during operation. Therefore, possibility of bioreactor’s control by means of changing temperature was proposed, analyzed, and implemented. A new supplementary input/output dynamical mathematical model, which considers influence of heating and cooling on a bioprocess, was developed. On a basis of this model, a control system was designed and a method for tuning of the controller was suggested. Results show characteristics, applicability, and advantages of the presented approach.

scholarly journals Assessment of Social Distancing for Controlling COVID-19 in Korea: An Age-Structured Modeling Approach

2020 ◽  
Vol 17 (20) ◽  
pp. 7474
Author(s):  
Yongin Choi ◽  
James Slghee Kim ◽  
Heejin Choi ◽  
Hyojung Lee ◽  
Chang Hyeong Lee
Keyword(s):  
Mathematical Model ◽  
Age Groups ◽  
Epidemiological Data ◽  
The Elderly ◽  
Model Parameters ◽  
Social Distancing ◽  
First Case ◽  
Age Structured ◽  
Epidemiological Characteristics ◽  
The Impact

The outbreak of the novel coronavirus disease 2019 (COVID-19) occurred all over the world between 2019 and 2020. The first case of COVID-19 was reported in December 2019 in Wuhan, China. Since then, there have been more than 21 million incidences and 761 thousand casualties worldwide as of 16 August 2020. One of the epidemiological characteristics of COVID-19 is that its symptoms and fatality rates vary with the ages of the infected individuals. This study aims at assessing the impact of social distancing on the reduction of COVID-19 infected cases by constructing a mathematical model and using epidemiological data of incidences in Korea. We developed an age-structured mathematical model for describing the age-dependent dynamics of the spread of COVID-19 in Korea. We estimated the model parameters and computed the reproduction number using the actual epidemiological data reported from 1 February to 15 June 2020. We then divided the data into seven distinct periods depending on the intensity of social distancing implemented by the Korean government. By using a contact matrix to describe the contact patterns between ages, we investigated the potential effect of social distancing under various scenarios. We discovered that when the intensity of social distancing is reduced, the number of COVID-19 cases increases; the number of incidences among the age groups of people 60 and above increases significantly more than that of the age groups below the age of 60. This significant increase among the elderly groups poses a severe threat to public health because the incidence of severe cases and fatality rates of the elderly group are much higher than those of the younger groups. Therefore, it is necessary to maintain strict social distancing rules to reduce infected cases.

scholarly journals Mathematical Model Predicts that Acceleration of Diabetic Wound Healing is Dependent on Spatial Distribution of VEGF-A mRNA (AZD8601)

2021 ◽  
Author(s):  
S. Michaela Rikard ◽  
Paul J. Myers ◽  
Joachim Almquist ◽  
Peter Gennemark ◽  
Anthony C. Bruce ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Wound Healing ◽  
Spatial Distribution ◽  
Surrounding Tissue ◽  
Diabetic Patients ◽  
Model Parameters ◽  
Diabetic Wound ◽  
Diabetic Wound Healing ◽  
Diabetic Wounds ◽  
The Impact

Abstract Introduction Pharmacologic approaches for promoting angiogenesis have been utilized to accelerate healing of chronic wounds in diabetic patients with varying degrees of success. We hypothesize that the distribution of proangiogenic drugs in the wound area critically impacts the rate of closure of diabetic wounds. To evaluate this hypothesis, we developed a mathematical model that predicts how spatial distribution of VEGF-A produced by delivery of a modified mRNA (AZD8601) accelerates diabetic wound healing. Methods We modified a previously published model of cutaneous wound healing based on coupled partial differential equations that describe the density of sprouting capillary tips, chemoattractant concentration, and density of blood vessels in a circular wound. Key model parameters identified by a sensitivity analysis were fit to data obtained from an in vivo wound healing study performed in the dorsum of diabetic mice, and a pharmacokinetic model was used to simulate mRNA and VEGF-A distribution following injections with AZD8601. Due to the limited availability of data regarding the spatial distribution of AZD8601 in the wound bed, we performed simulations with perturbations to the location of injections and diffusion coefficient of mRNA to understand the impact of these spatial parameters on wound healing. Results When simulating injections delivered at the wound border, the model predicted that injections delivered on day 0 were more effective in accelerating wound healing than injections delivered at later time points. When the location of the injection was varied throughout the wound space, the model predicted that healing could be accelerated by delivering injections a distance of 1–2 mm inside the wound bed when compared to injections delivered on the same day at the wound border. Perturbations to the diffusivity of mRNA predicted that restricting diffusion of mRNA delayed wound healing by creating an accumulation of VEGF-A at the wound border. Alternatively, a high mRNA diffusivity had no effect on wound healing compared to a simulation with vehicle injection due to the rapid loss of mRNA at the wound border to surrounding tissue. Conclusions These findings highlight the critical need to consider the location of drug delivery and diffusivity of the drug, parameters not typically explored in pre-clinical experiments, when designing and testing drugs for treating diabetic wounds.

scholarly journals Modelling Blood and Pulmonary Pressure for Solving a Performance Optimal Problem for Sportsmen

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
Jean Marie Ntaganda
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Comparative Study ◽  
Model Parameters ◽  
Stability Conditions ◽  
Nonlinear Ordinary Differential Equations ◽  
Respiratory Parameters ◽  
Blood Pressures ◽  
The Impact ◽  
Found Model

This paper aims at designing a three-compartmental mathematical model for determining the impact and response of blood pressures on cardiovascular and respiratory parameters. Three nonlinear ordinary differential equations are derived from three compartments. Stability conditions are established and inverse techniques are proposed for identifying model parameters. To test the efficiency of the found model, a validation is achieved based on an existing mathematical model through a comparative study.

A region-based mathematical model of the urine concentrating mechanism in the rat outer medulla. I. Formulation and base-case results

2005 ◽  
Vol 289 (6) ◽  
pp. F1346-F1366 ◽  
Author(s):  
Anita T. Layton ◽  
Harold E. Layton
Keyword(s):  
Mathematical Model ◽  
Rat Kidney ◽  
Tubuloglomerular Feedback ◽  
Transepithelial Transport ◽  
Base Case ◽  
Model Parameters ◽  
Outer Medulla ◽  
Concentrating Mechanism ◽  
The Impact ◽  
Urine Concentrating Mechanism

We have developed a highly detailed mathematical model for the urine concentrating mechanism (UCM) of the rat kidney outer medulla (OM). The model simulates preferential interactions among tubules and vessels by representing four concentric regions that are centered on a vascular bundle; tubules and vessels, or fractions thereof, are assigned to anatomically appropriate regions. Model parameters, which are based on the experimental literature, include transepithelial transport properties of short descending limbs inferred from immunohistochemical localization studies. The model equations, which are based on conservation of solutes and water and on standard expressions for transmural transport, were solved to steady state. Model simulations predict significantly differing interstitial NaCl and urea concentrations in adjoining regions. Active NaCl transport from thick ascending limbs (TALs), at rates inferred from the physiological literature, resulted in model osmolality profiles along the OM that are consistent with tissue slice experiments. TAL luminal NaCl concentrations at the corticomedullary boundary are consistent with tubuloglomerular feedback function. The model exhibited solute exchange, cycling, and sequestration patterns (in tubules, vessels, and regions) that are generally consistent with predictions in the physiological literature, including significant urea addition from long ascending vasa recta to inner-stripe short descending limbs. In a companion study (Layton AT and Layton HE. Am J Physiol Renal Physiol 289: F1367–F1381, 2005), the impact of model assumptions, medullary anatomy, and tubular segmentation on the UCM was investigated by means of extensive parameter studies.

scholarly journals Mathematical modeling of the transmission of SARS-CoV-2 ″ Evaluating the impact of isolation in São Paulo State (Brazil) and lockdown in Spain associated with protective measures on the epidemic of covid-19

2020 ◽  
Author(s):  
Hyun Mo Yang ◽  
Luis Pedro Lombardi ◽  
Fabio Fernandes Morato Castro ◽  
Ariana Campos Yang
Keyword(s):  
Mathematical Model ◽  
Sao Paulo ◽  
World Health ◽  
Model Parameters ◽  
São Paulo ◽  
Fatality Rate ◽  
Protective Measures ◽  
Paulo State ◽  
São Paulo State ◽  
The Impact

Coronavirus disease 2019 (covid-19), with the fatality rate in elder (60 years old or more) being much higher than young (60 years old or less) patients, was declared a pandemic by the World Health Organization on March 11, 2020. Taking into account this age-dependent fatality rate, a mathematical model considering young and elder subpopulations was formulated based on the natural history of covid-19 to study the transmission of the SARS-CoV-2. This model can be applied to study the epidemiological scenario resulting from the adoption of isolation or lockdown in many countries to control the rapid propagation of covid-19. We chose as examples the isolation adopted in São Paulo State (Brazil) in the early phase but not at the beginning of the epidemic, and the lockdown implemented in Spain when the number of severe covid-19 cases was increasing rapidly. Based on the data collected from Sa ̃o Paulo State and Spain, the model parameters were evaluated and we obtained higher estimation for the basic reproduction number R0 (9.24 for São Paulo State, and 8 for Spain) compared to the currently accepted estimation of R0 around 3. The model allowed to explain the flattening of the epidemic curves by isolation in São Paulo State and lockdown in Spain when associated with the protective measures (face mask and social distancing) adopted by the population. However, a simplified mathematical model providing lower estimation for R0 did not explain the flattening of the epidemic curves. The implementation of the isolation in Sa ̃o Paulo State before the rapidly increasing phase of the epidemic enlarged the period of the first wave of the epidemic and delayed its peak, which are the desirable results of isolation to avoid the overloading in the health care system.

scholarly journals Use of a Heating System to Control the Probiotic Beverage Production in Batch Bioreactor

2020 ◽  
Vol 11 (1) ◽  
pp. 84
Author(s):  
Jožef Ritonja ◽  
Andreja Goršek ◽  
Darja Pečar
Keyword(s):  
Control System ◽  
Fermentation Process ◽  
Closed Loop ◽  
Closed Loop Control ◽  
Loop Control ◽  
Batch Bioreactor ◽  
Closed Loop Control System ◽  
Loop Control System ◽  
The Impact

Fermentation is a crucial bioengineering process, existentially important for modern society. The most commonly used production unit for this process is the batch bioreactor. Its main advantage is unsophisticated construction, which unfortunately results in its incapability of controlling the transient state of the fermentation process. Control of the fermentation can significantly improve the quality of the product and the economy of the process; therefore, it is useful for bioreactors to be equipped with a control system. Based on the experimental results, we used an optimization method to identify a mathematical model that describes the impact of the bioreactor’s temperature on the fermentation’s transient process. The obtained model was applied for the design and synthesis of the closed-loop control system. Simulations and experiments confirmed the effectiveness of the proposed control system. In this way, we can ensure the consistent quality of the produced probiotic product, increase the amount of the product, and shorten the fermentation time. The original results display the feasibility of the closed-loop control of the batch bioreactor’s fermentation process by changing the temperature. So far, the process has been carried without a closed-loop control system. The problem is current and has not yet been solved sufficiently. There are many attempts published; one of the last shows the possibility of controlling the fermentation process by changing the oxygen supply, which is more complex and expensive for realization than the solution from our study.

A Mathematical Model for the Study of Effectiveness in Therapy in Tuberculosis Taking into Account Associated Diseases

2021 ◽  
Author(s):  
Erick Delgado Moya ◽  
Alain Pietrus ◽  
Sergio Muniz Oliva
Keyword(s):  
Mathematical Model ◽  
Negative Impact ◽  
Population Based ◽  
The Other ◽  
Model Parameters ◽  
Tb Treatment ◽  
Mdr Tb ◽  
And Control ◽  
The Impact ◽  
Hiv Aids

Tuberculosis (TB) remains a major global health problem. We present a deterministic mathematical model for the study of the effectiveness of therapy in TB to determine the impact of HIV/AIDS and diabetes in the spread of the disease and drug resistance. Our model takes into account the relationships between TB, HIV/AIDS, and diabetes and we also study the behavior of multidrug-resistance (MDR-TB) and extensively drug-resistant (XDR-TB). The main mathematical and epidemiology features of the model are investigated. The basic reproduction number (R0) in the different sub-populations (diabetics, HIV/AIDS, and those who do not suffer from these diseases) was studied. Conditions were obtained on the model parameters to know when the growth of the parameters associated with resistance to TB treatment has a negative impact on the transmission of TB in the population based on the R0 study. It is concluded that MDR-TB and XDR-TB have a negative impact on TB control. Computational simulations show that a greater number of drug-sensitive TB cases with respect to MDR-TB and XDR-TB cases are reported in the infected compartments, and MDR-TB cases surpass XDR-TB cases, except in the diabetes sub-population, which has a growth of XDR-TB cases that surpasses the other compartments of infected of all the sub-populations. It was shown when comparing the sub-populations of diabetes and HIV/AIDS, that although the diabetes sub-population reports a higher number of XDR-TB cases, a lower number of drug-sensitive TB and MDR-TB cases, have a greater number of recovered cases with respect to HIV/AIDS sub-population at the end of the study period. Also, when the XDR-TB cases in the diabetes sub-population exceed the other infected compartments, there is a growth of recovered TB in this subpopulation. The results suggest that it is necessary to increase the attention to the diabetic population, which include improved glucose control, increase the number of specialized medical consultations to achieve permanence in TB treatment and control the entry of individuals to the diabetic compartments by tests of diabetes.

scholarly journals Assessing the effects of global warming and local social and economic conditions on the malaria transmission

2000 ◽  
Vol 34 (3) ◽  
pp. 214-222 ◽  
Author(s):  
Hyun M Yang ◽  
Marcelo U Ferreira
Keyword(s):  
Mathematical Model ◽  
Global Warming ◽  
Steady State ◽  
Malaria Transmission ◽  
Compartmental Model ◽  
Economic Conditions ◽  
Risk Level ◽  
Temperature Changes ◽  
Dynamic Analyses ◽  
The Impact

OBJECTIVE: To show how a mathematical model can be used to describe and to understand the malaria transmission. METHODS: The effects on malaria transmission due to the impact of the global temperature changes and prevailing social and economic conditions in a community were assessed based on a previously presented compartmental model, which describes the overall transmission of malaria. RESULTS/CONCLUSIONS: The assessments were made from the scenarios produced by the model both in steady state and dynamic analyses. Depending on the risk level of malaria, the effects on malaria transmission can be predicted by the temperature ambient or local social and-economic conditions.

scholarly journals Evaluating the impacts of release in São Paulo State (Brazil) on the epidemic of covid-19 based on mathematical model

2020 ◽  
Author(s):  
Hyun Mo Yang ◽  
Luis Pedro Pedro Lombardi Junior ◽  
Ariana Campos Yang ◽  
Fabio Fernandes Morato Castro
Keyword(s):  
Mathematical Model ◽  
Sao Paulo ◽  
Model Parameters ◽  
Isolated Population ◽  
São Paulo ◽  
Paulo State ◽  
History Of ◽  
São Paulo State ◽  
Using Data ◽  
The Impact

To flatten the curve of the natural epidemic of covid-19, many countries adopted lockdown or isolation resulting in the containment of the SARS-CoV-2 transmission. However, an important question arises about the strategies of release of isolated persons to avoid overloaded hospitals and increased deaths. São Paulo State (Brazil) implemented the isolation of the population in non- essential activities on March 24, and the progressive flexibilization considering the characteristics of each location (release of the isolated population) initiated on June 15. A mathematical model based on the natural history of covid-19 was applied to describe the epidemiological scenario with isolation in São Paulo State, and assess the impact of release on the covid-19 epidemic. Using data collected from São Paulo State, we estimated the model parameters to obtain the curves of the epidemic, the number of deaths, and the clinical evolution of covid-19. The epidemic under isolation was the framework to evaluate the strategies of the release, that is, how these curves are changed with the release of isolated persons. We evaluated three strategies of release. First two strategies considered four releases in the isolated population in four equal proportions, but successive releases elapsed by 14 and 21 days. In each strategy the beginning of the release was on June 29 and July 13, when the effective reproduction number Ref was evaluated. The third strategy aimed at the protection of the elder subpopulation. We observed that the delay to begin the release and the increased elapse between successive releases resulted in a better scenario by decreasing severe covid-19 cases and, consequently, to avoid overloaded hospitals. We also observed that the release delayed to achieve lower values for Ref and infectious persons retarded in several months the quick increasing phase of the forthcoming epidemic. However, this epidemic can be flattened or even suppressed by isolation of infectious persons by mass testing and/or by rigid adoption of protective measures and social distancing.

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