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At least 487 records · Page 27Linked to original sources
PubMed1999

Mathematical modeling of lipase and protease production by Penicillium restrictum in a batch fermenter.

This work presents a mathematical model that describes time course variations of extracellular lipase and protease activities for the batch fermentation of the fungus Penicillium restrictum, a new and promising strain isolated from soil and wastes of a Brazilian babassu coconut oil industry. The fermentation process was modeled by an unstructured model, which considered the following dependent variables: cells, fat acid, dissolved oxygen concentrations, lipase and protease activities, and cell lysate concentration. The last variable represents the amount of cells that has been lysed by the shear stress and natural cell death. Proteases released to the medium, as consequence of this process, enhance lipase inactivation. The model is able to predict the effects of some operation variables such as air flow rate and agitation speed. The mathematical model was validated against batch-fermentation data obtained under several operating conditions. Because substrate concentration has antagonistic effects on lipase activity, a typical optimization scheme should be developed in order to minimize these deleterious effects while maximizing lipase activity.

Journal Article↗
PubMed1990

Mathematical models of sow reproduction.

Nutrition affects reproduction, but the physiological mechanisms are not known. Defining those mechanisms is a high priority for animal scientists. This paper briefly describes mathematical models developed to aid in elucidating those mechanisms and which may be applied to predict animal performance. Two types of mechanistic mathematical models of sows are described, based respectively on nutrient partitioning and on metabolic and physiological principles. The nutrient partitioning model is relatively mature but the metabolic/physiological model is still at an early stage of development. The use of such models in the design and evaluation of feeding programmes, in understanding the biological system and in improving research efficiency are outlined. These two models are now being used as described, and it is anticipated that they, and other models, will make important contributions to the marked improvements in reproductive performance in commercial pig production that is anticipated during the next few years.

Animals↗
PubMed1999

Mathematical modelling of morphogenesis in fungi: a key role for curvature compensation ('autotropism') in the local curvature distribution model.

The assumption that the mushroom stem has the ability to undergo autonomic straightening enables a mathematical model to be written that accurately mimics the gravitropic reaction of the stems of Coprinus cinereus. The straightening mechanism is called curvature compensation here, but is equivalent to the 'autotropism' that often accompanies the gravitropic reactions of axial organs in plants. In the consequently revised local curvature distribution model, local bending rate is determined by the difference between the 'bending signal' (generated by gravitropic signal perception systems) and the 'straightening signal' (proportional to the local curvature at the given point). The model describes gravitropic stem bending in the standard assay with great accuracy but has the virtue of operating well outside the experimental data set used in its derivation. It is shown, for example, that the mathematical model can be fitted to the gravitropic reactions of stems treated with metabolic inhibitors by a change of parameters that parallel the independently derived physiological interpretation of inhibitor action. The revised local curvature distribution model promises to be a predictive tool in the further analysis of gravitropism in mushrooms.

Calcimycin↗
PubMed1998

Mathematical modelling as a tool to study population dynamics between sulfate reducing and methanogenic bacteria.

The existing mathematical models of sulphate fed anaerobic reactors are reviewed. Special attention was put on pecularities of the description of sulphide inhibition and competition between sulphate reduction and methanogenesis in such systems. The paper also presents an integrated mathematical model of the functioning of a sulphate fed granular sludge reactor taking into account concentration gradients on substrates, intermediates, products and bacteria inside the reactor as well as multiple-reaction stoichiometry and kinetics. The developed model includes the following blocks: a) hydrodynamic block describing liquid flow as well as transport and distribution of the components along the reactor height; b) kinetic block including growth, metabolism, inhibition and competition of acidogenic, acetogenic, methanogenic and sulphate reducing bacteria in the system; c) physico-chemical block for calculation of pH in each compartment of the liquid phase; d) transfer block describing a mass transfer of gaseous components from the liquid to the gas phase. The integrated model was calibrated and validated using laboratory studies on the functioning of sulphidogenic granular sludge reactors, i.e. their start-up and the maximization of sulphide yield in these reactors. The modelling of the reactor operation is supplemented with hypothetical computer simulations to illustrate the influence of engineering parameters on the operation performance and sulphate conversion of sulphidogenic reactors.

Algorithms↗
PubMed2006

[Combating infectious disease using mathematical modelling].

When determining interventions against threatening infectious diseases such as HIV-infection, severe acute respiratory syndrome (SARS), smallpox and pandemic influenza, the use of mathematical models of the spread of infectious diseases is becoming increasingly popular. These models contribute to the structuring of the knowledge already available in various disciplines, to finding epidemiological connnections, to demonstrating lacunas within the pool of knowledge and to the comparison of the expected effects and costs of preventative and intervention measures. The use of models leads to a 'made-to-measure' analysis ofthe effects and costs of preventative and intervention measures which takes account of the specific characteristics of infectious diseases. The integration of knowledge from various disciplines can be supported by more research into the theoretical epidemiology of infectious disease and by better integration of mathematical models into policy development. The resulting and better foundations of this policy that are achieved by means of infectious disease modelling translate into more effective combating of infectious disease.

Cost-Benefit Analysis↗
PubMed2005

Mathematical model for optimal control in wastewater discharges: the global performance.

In this work we show how mathematical models and optimal control techniques can help us to solve some problems of environmental engineering, more precisely, water pollution problems arising from wastewater discharges into coastal areas or rivers. We deal with a complete two-dimensional mathematical model for the evolution of pollutant concentration in a shallow water domain. By integrating this model we obtain a zero-dimensional one and we use it to study the global performance of the system in a realistic situation. Finally, by using the two-dimensional model, we recall two optimal control problems related to the wastewater disposal problem.

Models, Theoretical↗
PubMed1989

Three-dimensional kinematic modelling of the human shoulder complex--Part II: Mathematical modelling and solution via optimization.

In this paper, individual joint sinus cones associated with the sternoclavicular, claviscapular, and glenohumeral joints of the three-dimensional kinematic model introduced in Part I for the human shoulder complex are quantitatively determined. First, mathematical description of the humerus orientation with respect to torso is given in terms of eight joint variables. Since the system is a kinematically redundant one, solution for the joint variables satisfying a prescribed humerus orientation is possible only if additional requirements are imposed; and the "minimum joint motion" criterion is introduced for this purpose. Two methods, namely the Lagrange multipliers and flexible tolerance methods, are formulated and tested for the optimization problem. The statistical in-vivo data base for the circumductory motion of the upper arm is employed to determine a set of joint variables via optimization, which are then utilized to establish the sizes and orientations of the elliptical cones for the individual joint sinuses. The results are discussed and compared with those given on the basis of measurements made on cadaveric specimens.

Biomechanical Phenomena↗
PubMed1973

A new mathematical model for fitting an HPL radioimmunoassay curve.

A number of mathematical models have been tested for their suitability in representing the dose response curve of a specific assay of the hormone human placental lactogen (HPL).(1)A new equation Y = B[0.14 + 1/[1 + C log [1 + exp[X - D]]] where Y is the percentage activity or counts bound to the antibody and X is the HPL concentration is proposed as representing the overall shape of the curve. This model is shown to give both an accurate representation of the curve and to allow reproducible determination of an unknown over a number of occasions. A number of other models are compared. The new model allows automatic calculation of HPL concentrations from a standard curve using a computer.

Computers↗
PubMed2003

Prediction of inspiratory flow shapes during sleep with a mathematic model of upper airway forces.

STUDY OBJECTIVES: To predict the airflow dynamics during sleep using a mathematic model that incorporates a number of static and dynamic upper airway forces, and to compare the numerical results to clinical flow data recorded from patients with sleep-disordered breathing on and off various treatment options. DESIGN: Upper airway performance was modeled in virtual subjects characterized by parameter settings that describe common combinations of risk factors predisposing to upper airway collapse during sleep. The treatments effect were induced by relevant changes of the initial parameter values. SETTING: Computer simulations at our website (http://www.utu.fi/ml/sovmat/bio/). PARTICIPANTS: Risk factors considered in the simulation settings were sex, obesity, pharyngeal collapsibility, and decreased phasic activity of pharyngeal muscles. INTERVENTIONS: The effects of weight loss, pharyngeal surgery, nasal continuous positive airway pressure, and respiratory stimulation on the inspiratory flow characteristics were tested with the model. MEASUREMENTS AND RESULTS: Numerical predictions were investigated by means of 3 measurable inspiratory airflow characteristics: initial slope, total volume, and flow shape. The model was able to reproduce the inspiratory flow shape characteristics that have previously been described in the literature. Simulation results also supported the observations that a multitude of factors underlie the pharyngeal collapse and, therefore, certain medical therapies that are effective in some conditions may prove ineffective in others. CONCLUSIONS: A mathematic model integrating the current knowledge of upper airway physiology is able to predict individual treatment responses. The model provides a framework for designing novel and potentially feasible treatment alternatives for sleep-disordered breathing.

Arousal↗
PubMed1983

A mathematical model for timing repeated medical tests.

This paper presents a mathematical model that can be used to estimate the clinical and economic outcomes of monitoring patients with periodic examinations. The model can compare the consequences of monitoring for different disorders, with different tests, at different frequencies. The paper describes formulas that incorporate information about the incidence and natural history of disorders, the effectiveness of tests, the effectiveness of treatment, and the order and frequency of monitoring, to calculate the probability of detecting a disorder, the method and timing of detection, the earliness (e.g., stage) with which a disorder is detected, and the clinical and economic outcomes. The application of the model is described through a hypothetical example. The model has been used to analyze several cancer screening problems involving multiple disorders and multiple tests.

Cost-Benefit Analysis↗
PubMedDate not supplied

[Mathematical modeling of the dynamics of biokinematic chains].

The method of mathematical modelling of the dynamics of biokinematic chains based on the application of Lagrange equations is considered. An algorythm of determining articulate moments in the matrix form. As an example of the biokinematic chain a model of man's upper extremity is considered. Correctness of the model and of the system of differential equations describing its dynamics is proved experimentally.

Arm↗
PubMed1975

Nonlinear regression methods in design of experiments and mathematical modelling. Applications to the analysis of the steady-state kinetics of glutathione reductase.

A branching reaction pathway involving a ping pong and a sequential loop has been proposed for glutathione reductase (Biochem. Biophys. Res. Commun. 53 (1973) 1151). In the present investigation nonlinear regression methods have been applied in the fitting of rate equations to experimental data to test the validity of the model proposed and to discriminate between alternative mathematical models (cf. FEBS Lett. 26 (1972) 252). In the best rate law, some of the parameters were numerically redundant. Therefore, a feature-wise analysis of the rate equation was carried out by varying one substrate concentration at a time. The overall strategy used was a cyclic procedure involving: experimentation - analysis of data - modelling - design of experiments - new experimentation etc. Consideration was given to the experimental error structure and to the importance of weighting in the regression analysis. In the design of experiments for discrimination between rival models, a previously defined discrimination function was used. The results of the analysis support the branching reaction scheme proposed for glutathione reductase.

Glutathione↗
PubMed2004

Mathematical modeling of granulocyte reconstitution after high-dose chemotherapy with stem cell support: effect of post-transplant G-CSF treatment.

Cancer patients treated with high-dose chemotherapy and autotransplanted with peripheral blood progenitor cells most often reconstitute neutrophils (> 0.5 x 10(9)c/l) 8-16 days after the initiation of treatment. By means of a mathematical model of human granulopoiesis, the present work assesses the effect of administering granulocyte colony stimulating factor (G-CSF) post-transplant to reduce engraftment time, and also assesses the effect of delaying initiation of G-CSF treatment relative to a general schedule. Hematopoietic progenitor cells from 21 breast cancer patients were mobilized by chemotherapy followed by G-CSF injections. Purified CD34+ cells taken from the mobilized blood were infused 3 days after termination of chemotherapy. Patients were given subcutaneous injections of G-CSF post-transplant (5 microg/kg every 12 h). Neutrophil counts calculated from a mathematical model were compared with data from individual patients. These results were also compared with data and modeling results from a group of 19 lymphoma patients given no post-transplant G-CSF therapy. The observed engraftment times were associated with the number of CFU-GM cells in the reinfused blood graft and the administration of post-transplant G-CSF. The latter finding was most predominant in patients given < 5.0 x 10(5) CFU-GM/kg bw. These tendencies were well captured by the model. Interestingly, the model showed no major differences in time to engraft neutrophils if the initiation of G-CSF was postponed for up to 5 days after transplantation. Our findings indicate that the present mathematical model of neutrophil recovery following high-dose therapy correlates with clinical observations and can potentially be used to predict time to neutrophil recovery.

Antineoplastic Agents↗
PubMed2005

A novel mathematical model identifies potential factors regulating bone apposition.

The development of pharmaceutical treatments for bone disease can be enhanced by mathematical models that predict their effects on matrix apposition during cancellous bone remodelling. Therefore, a mathematical model was constructed to simulate the rate of focal bone formation from the number of osteoid-forming osteoblasts at one microsite and their rate of activity. The number of mature osteoid-forming cells was simulated from a relationship describing the proliferation of preosteoblasts. Osteoblast activity was described by Michaelis-Menten enzyme kinetic equations adapted to describe cellular activity. The model incorporates the negative feedback effects on the rates of bone apposition due to the reduction in size of mature osteoblasts with continuing differentiation and the reduction in number of osteoid-forming cells with apoptosis and osteocyte formation. In addition, the rate of mineralisation is limited according to osteoid substrate availability. Results of sensitivity analysis revealed the amount of bone formed at one microsite to be more sensitive to changes in factors that controlled cell growth during proliferation and the number of mature osteoid-forming osteoblasts than to those that determined cellular activity. Matrix and osteocyte signalling were shown to have potentially important roles in controlling rates of osteoid apposition in normal, healthy bone. This simple model supports the critical role of controlled mitotic growth in normal bone apposition. It can also help to explain how the homeostatic processes of bone resorption and apposition during remodelling can be disrupted by growth factors that affect the mitotic fraction and division time of proliferative preosteoblast cells.

Cell Proliferation↗
PubMed1994

Mathematical model for the mineralization of bone.

A mathematical model is presented for the transport and precipitation of mineral in refilling osteons. One goal of this model was to explain calcification "halos," in which the bone near the haversian canal is more highly mineralized than the more peripheral lamellae, which have been mineralizing longer. It was assumed that the precipitation rate of mineral is proportional to the difference between the local concentration of calcium ions and an equilibrium concentration and that the transport of ions is by either diffusion or some other concentration gradient-dependent process. Transport of ions was assumed to be slowed by the accumulation of mineral in the matrix along the transport path. The model also mimics bone apposition, slowing of apposition during refilling, and mineralization lag time. It was found that simple diffusion cannot account for the transport of calcium ions into mineralizing bone, because the diffusion coefficient is two orders of magnitude too low. If a more rapid concentration gradient-driven means of transport exists, the model demonstrates that osteonal geometry and variable rate of refilling work together to produce calcification halos, as well as the primary and secondary calcification effect reported in the literature.

Animals↗
PubMed1997

Mathematical model of progressive renal disease.

A simple mathematical model is proposed that predicts the dynamics of chronic progressive renal disease. The model consists of coupled linear differential equations formed from three state variables, four control parameters, and three parameters related to initial conditions. All have straightforward physical interpretations. Applied to a population of nephrons, the model predicted the hypertrophic and sclerotic features of parenchyma progressing towards end-stage renal disease. Simulation results compared favorably with measurements obtained from the literature involving the subtotal nephrectomy rat model for renal disease. The time course of disease progression and treatment were considered. Also, the implications of the model for designing new diagnostic techniques using ultrasonic analysis are discussed.

Disease Progression↗
PubMedDate not supplied

Studies of long-term potentiation and depression of inhibitory transmission by mathematical modeling of post-synaptic processes.

A mathematical model of posttetanic processes launched by rhythmic stimulation of the excitatory and inhibitory inputs to the dendritic spine of a pyramidal neuron in hippocampal field CA3 was used to study conditions for modifying the efficiency of the inhibitory input. The level of dephosphorylation of GABAa and GABAb receptors, which determines the GABA sensitivity of these receptors, was shown to depend on the Ca(2+)-dependent ratio of active protein kinases and protein phosphatases; the level of dephosphorylation decreased monotonically as the intracellular Ca2+ increased. Posttetanic increases and decreases in the Ca2+ concentration, as compared with the level achieved during the previous stimulation, led to increases or decreases respectively in the number of dephosphorylated GABA receptors and to induction of long-term potentiation and depression, respectively, in the efficiency of inhibitory transmission. The extent of the modification effect depended on the ratio of the quantities of inhibitory and excitatory mediators in the synaptic cleft. At very low or very high GABA concentrations, modification of inhibitory transmission was insignificant.

Algorithms↗
PubMed1996

A mathematical model of the pancreatic ductal epithelium.

A mathematical model of the HCO-3-secreting pancreatic ductal epithelium was developed using network thermodynamics. With a minimal set of assumptions, the model accurately reproduced the experimentally measured membrane potentials, voltage divider ratio, transepithelial resistance and short-circuit current of nonstimulated ducts that were microperfused and bathed with a CO2/HCO-3-free, HEPES-buffered solution, and also the intracellular pH of duct cells bathed in a CO2/HCO-3-buffered solution. The model also accurately simulated: (i) the effect of step changes in basolateral K+ concentration, and the effect of K+ channel blockers on basolateral membrane potential; (ii) the intracellular acidification caused by a Na+-free extracellular solution and the effect of amiloride on this acidification; and (iii) the intracellular alkalinization caused by a Cl--free extracellular solution and the effect of DIDS on this alkalinization. In addition, the model predicted that the luminal Cl- conductance plays a key role in controlling both the HCO-3 secretory rate and intracellular pH during HCO-3 secretion. We believe that the model will be helpful in the analysis of experimental data and improve our understanding of HCO-3-transporting mechanisms in pancreatic duct cells.

Animals↗