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PubMed2003

Mathematical modeling relevant to closed artificial ecosystems.

The mathematical modeling of ecosystems has contributed much to the understanding of the dynamics of such systems. Ecosystems can include not only the natural variety, but also artificial systems designed and controlled by humans. These can range from agricultural systems and activated sludge plants, down to mesocosms, microcosms, and aquaria, which may have practical or research applications. Some purposes may require the design of systems that are completely closed, as far as material cycling is concerned. In all cases, mathematical modeling can help not only to understand the dynamics of the system, but also to design methods of control to keep the system operating in desired ranges. This paper reviews mathematical modeling relevant to the simulation and control of closed or semi-closed artificial ecosystems designed for biological production and recycling in applications in space.

Animals↗
PubMed2006

Simple stochastic fingerprints towards mathematical modeling in biology and medicine 2. Unifying Markov model for drugs side effects.

Most of present mathematical models for biological activity consider just the molecular structure. In the present article we pretend extending the use of Markov chain models to define novel molecular descriptors, which consider in addition other parameters like target site or biological effect. Specifically, this mathematical model takes into consideration not only the molecular structure but the specific biological system the drug affects too. Herein, a general Markov model is developed that describes 19 different drugs side effects grouped in eight affected biological systems for 178 drugs, being 270 cases finally. The data was processed by linear discriminant analysis (LDA) classifying drugs according to their specific side effects, forward stepwise was fixed as strategy for variables selection. The average percentage of good classification and number of compounds used in the training/predicting sets were 100/95.8% for endocrine manifestations, (18 out of 18)/(13 out of 14); 90.5/92.3% for gastrointestinal manifestations, (38 out of 42)/(30 out of 32); 88.5/86.5% for systemic phenomena, (23 out of 26)/(17 out of 20); 81.8/77.3% for neurological manifestations, (27 out of 33)/(19 out of 25); 81.6/86.2% for dermal manifestations, (31 out of 38)/(25 out of 29); 78.4/85.1% for cardiovascular manifestation, (29 out of 37)/(24 out of 28); 77.1/75.7% for breathing manifestations, (27 out of 35)/(20 out of 26) and 75.6/75% for psychiatric manifestations, (31 out of 41)/(23 out of 31). Additionally a back-projection analysis (BPA) was carried out for two ulcerogenic drugs to prove in structural terms the physical interpretation of the models obtained. This article develops a mathematical model that encompasses a large number of drugs side effects grouped in specifics biological systems using stochastic absolute probabilities of interaction ((A)pi(k)(j)) by the first time.

Drug-Related Side Effects and Adverse Reactions↗
PubMed2005

An application of Lacker's mathematical model for the prediction of ovarian response to superstimulation.

Introduction. A mathematical model of ovarian follicular growth is applied to the problem of predicting ovarian response in a superstimulation protocol. Methods. Fifty-four women enrolled in an ovarian superstimulation program of therapy for the amelioration of idiopathic infertility had their ovarian cycles synchronized by taking Demulen 30 for two weeks prior to the study. Daily ultrasonographic imaging, measurements of serum estradiol and doses of hMG began on day 5 after the patients stopped taking Demulen. The diameters of individual follicles were measured and followed daily. When the largest follicle attained a diameter of 19 mm, hCG was given to induce ovulation. Individual follicle growth data were fit to a mathematical model of ovarian follicle maturation and the resulting parameters were used to classify patients into low and high ovarian response groups. Results. The parameters computed from the mathematical model fit were found to be predictive of ovarian response with a sensitivity of 71% and a specificity of 70%. The parameters were also meaningful within the context of the original mathematical model and have value for determining how doses of hMG may be adjusted during the course therapy to increase the ovarian response in individuals. Conclusion. Mathematical modeling of ultrasonographically derived follicular growth data has significant potential for clinical application in ovarian superstimulation protocols. The method of fitting follicular growth data to a mathematical follicle maturation surface furthermore provides a straightforward approach for the characterization of ovarian follicular dynamics in general.

Adult↗
PubMed2005

Mathematical modelling of small wastewater treatment plants: power and limitations.

Although mathematical modelling of biological wastewater treatment processes has proved to be valuable for large-scale WWTPs (wastewater treatment plants) little experience has been acquired in the mathematical modelling of small wastewater treatment plants. This paper seeks to evaluate the applicability of mathematical modelling on small systems, which are characterized by high fluctuations in organic and hydraulic loads and little possibility for control. In order to achieve this, the paper examines the different steps in a general modelling protocol. One important bottleneck for the general use of mathematical modelling of small systems that emerges is the frequent sampling and many analyses needed for characterization of the flows while its applicability is limited. On the other hand, the determination of the model structure of a small WWTP can be quite valuable. Experiments show that tracer tests should include tests with a highly varying influent flow rate to spot independent small internal flows as these can have a significant impact on the behaviour of peak concentrations throughout the system. In addition, the model structure determination can provide useful information on dead zones, short-circuiting and mixing behaviour in the plant.

Models, Theoretical↗
PubMed2003

Formulation of a mathematical model to predict solar water disinfection.

A mathematical model was formulated that will facilitate the prediction of solar disinfection by analyzing the effect of sunlight exposure (x(1)) and the load of bacterial contamination (x(2)), as predictor variables, on the efficiency of solar disinfection (y). Aliquots of 0.1 ml containing average numbers of E. coli, ranging between 1 and 5 x 10(3)cells/ml raw water, were introduced into each of the 96 wells of polystyrene microtitre plates. Plates, with the lid on, were exposed to sunlight for varying exposures ranging between 1.04 x 10(3) and 8.40 x 10(3)kJ m(-2). Double strength nutrient broth was then added. After 48 h incubation wells containing visible contamination were considered as containing one cell or more that survived the exposure. Data showed that disinfection is dependent both on the load of bacterial contamination and sunlight exposure. This relationship is characterized by curves having shoulders followed by a steep decline and then tailing off in an asymptotic fashion. The shoulder size increased with the increase of the contamination load, however, the slope remains the same. Statistical analysis indicates a positive correlation among the variables (R(2) = 0.893); the mathematical model, y=1-(1-e(-kx(1)))(x(2)), represents the relationship, with k being the solar inactivation constant. The exposure required to produce a given decontamination level can be predicted using the equation: x(1)=-1/kln[1-(1-y)(-1/x(2))]e(-micro/rho.m/A), where micro is the linear attenuation coefficient (m(-1)), rho is the density, m is the mass and A is the area of the exposed part of the sample. The predictor variables (x(1), x(2)) strongly influence the efficiency of solar disinfection, which can be predicted using the suggested mathematical model. The present data provides a means to predict the efficiency of solar disinfection as an approach to improve the quality of drinking water mainly in developing countries with adequate sunshine all year-round.

Disinfection↗
PubMed1994

Evaluation of a mathematical model for predicting the relationship between protein and energy intakes of low-birth-weight infants and the rate and composition of weight gain.

A model for predicting the relationship between protein and energy intakes of low-birth-weight (LBW) infants and the rate and composition of weight gain is described. It is based on linear multiple regression equations summarizing the rates of weight gain, nitrogen retention, and energy retention of 101 previously studied LBW infants fed protein intakes ranging from 2.25 to 3.9 g.kg-1.d-1 and concomitant energy intakes ranging from 115 to 147 kcal.kg-1.d-1 plus current theory concerning nutrient retention and body composition. To test the validity of the model, three combinations of protein and energy intake predicted by the model to result in specific rates and compositions of weight gain were fed to 44 LBW infants, and the observed rates of weight gain, protein accretion, and fat accretion were compared with the rates predicted by the model. Differences in these and other outcome variables between two of the groups, the intakes of which differed only in energy, also were compared to provide additional insight into the effect of concomitant energy intake on protein utilization. Across groups, actual outcomes correlated closely with predicted outcomes, supporting the validity of the model for the total population. However, outcomes of individual infants deviated as much as 30% from predicted outcomes; the magnitude of the deviation was independent of birth weight, gestational age, or size for gestational age.(ABSTRACT TRUNCATED AT 250 WORDS)

Body Composition↗
PubMed1981

A mathematical model for the analysis of the turnover of protein mixtures. II. Modified power functions as special models.

In part 1 of this series a model for the protein turnover characterized by an inhomogeneous protein pool with a distribution of turnover constants was developed. This model is mathematically described, taking into account that the protein turnover is experimentally determined almost exclusively by tracer experiments, but a system of integro-differential equations. The analytical solution of this system of equations is elaborated for 3 special cases: tracer elimination from the protein pool after pulse labelling, tracer accumulation due to continuous labelling, and elimination after stopping this continuous incorporation of tracer. The applicability of the resulting modified power function is tested using an example for the literature (Garlic et al.: Biochem. J. 156, 657 (1976)) and computer generated data. On this background the existence of several classes of proteins computer generated data. On this background the existence of several classes of proteins with typical life times is discussed. Finally, the general applicability of power functions for tracer kinetic problems is treated from the point fo view of the results obtained in this paper.

Kinetics↗
PubMed1998

A mathematical model of drug resistance: heterogeneous tumors.

A mathematical model is developed to describe the growth and control of a heterogeneous tumor. The main aspect of the model is that it takes into account induced drug resistance. The mathematical model is a system of two ordinary differential equations that describes the growth of the cancer along with the effects of chemotherapy. The model is analyzed to determine what some of the critical parameters are; how we determine an effective treatment; how combination chemotherapy should be delivered; and how this model may help us develop more effective cancer chemotherapeutic treatments.

Animals↗
PubMed1992

Epidemiology, HIV and drugs: mathematical models and data.

The utility of mathematical models in understanding the dynamics of HIV transmission among injecting drug users (IDUs) and their non-IDU sex partners is discussed. We emphasize the need for collaborative relationships between modellers and drug-use researchers, and we stress that models should be based on data in both their formulation and development stages. We outline some of the possible data requirements of transmission models and we highlight the need for the collection of appropriate quantitative data, so that modellers can estimate specific parameters for their models. We believe that discussion of the needs and utility of mathematical modelling will lead to mutually beneficial collaborations between theoreticians and drug-use researchers. These collaborations may aid in the design and the evaluation of effective behavioural or medical intervention strategies.

England↗
PubMed1980

A mathematical model for the curves of intrauterine growth.

Different mathematical models for a chart of intrauterine growth were tested attempting to employ uncomplicated curves. In this manner, a chart of foetal growth was elaborated by plotting the cube root of neonate weight against the gestational age. Two different regions can be clearly seen in this chart of growth. In the first one, until the 34th week of pregnancy, there is a linear relationship between the two variables. In the second region, for pregnancies above the 34th week, the curve has a quadratic equation, reaching the maximum between the 43rd and 44th week, decreasing posteriorly. The goodness of fit obtained by the present mathematical model is more satisfactory than that obtained by mathematical models with a single linear equation.

Anthropometry↗
PubMed1991

Analysis of chemotactic bacterial distributions in population migration assays using a mathematical model applicable to steep or shallow attractant gradients.

The mathematical model developed by Rivero et al. (1989, Chem. Engng Sci. 44, 2881-2897) is applied to literature data measuring chemotactic bacterial population distributions in response to steep as well as shallow attractant gradients. This model is based on a fundamental picture of the sensing and response mechanisms of individual bacterial cells, and thus related individual cell properties such as swimming speed and tumbling frequency to population parameters such as the random motility coefficient and the chemotactic sensitivity coefficient. Numerical solution of the model equations generates predicted bacterial density and attractant concentration profiles for any given experimental assay. We have previously validated the mathematical model from experimental work involving a step change in the attractant gradient (Ford et al., 1991 Biotechnol. Bioengng, 37, 647-660; Ford and Lauffenburger, 1991, Biotechnol. Bioengng, 37, 661-672). Within the context of this experimental assay, effects of attractant diffusion and consumption, random motility, and chemotactic sensitivity on the shape of the profiles are explored to enhance our understanding of this complex phenomenon. We have applied this model to various other types of gradients with successful interpretation of data reported by Dalquist et al. (1972, Nature New Biol. 236, 120-123) for Salmonella typhimurium validating the mathematical model and supporting the involvement of high and low affinity receptors for serine chemotaxis by these cells.

Bacterial Physiological Phenomena↗
PubMed2004

Mathematical modeling reveals threshold mechanism in CD95-induced apoptosis.

Mathematical modeling is required for understanding the complex behavior of large signal transduction networks. Previous attempts to model signal transduction pathways were often limited to small systems or based on qualitative data only. Here, we developed a mathematical modeling framework for understanding the complex signaling behavior of CD95(APO-1/Fas)-mediated apoptosis. Defects in the regulation of apoptosis result in serious diseases such as cancer, autoimmunity, and neurodegeneration. During the last decade many of the molecular mechanisms of apoptosis signaling have been examined and elucidated. A systemic understanding of apoptosis is, however, still missing. To address the complexity of apoptotic signaling we subdivided this system into subsystems of different information qualities. A new approach for sensitivity analysis within the mathematical model was key for the identification of critical system parameters and two essential system properties: modularity and robustness. Our model describes the regulation of apoptosis on a systems level and resolves the important question of a threshold mechanism for the regulation of apoptosis.

Apoptosis↗
PubMed1980

The use of a mathematical model in rhinomanometry.

The authors consider the mathematical model proposed by the Swedish Group (Broms et al.). This model permits the pressure gradient-flow recording as obtained from anterior or posterior rhinomanometry to be converted into a mathematical formula. The model was tested for its mathematical, statistical, and clinical utility with 32 normal test subjects. It is the conviction of the authors, although not totally without reservation, that this is the best mathematical model in existence.

Adolescent↗
PubMed1996

On the dangers of adjusting the parameters values of mechanism-based mathematical models.

Mechanism-based mathematical models describe systems in terms of identifiable physical processes, and the parameters are assumed to have fundamental physical significance. Ideally, the parameter values are measured independent of the system being modeled, but these values are often adjusted to give the best fit of model predictions to experimental data. A systematic investigation of the effects of such parameter adjustment was conducted by developing a model system comprising a known reaction mechanism and known rate constants. Simulations of experiments were run, and then attempts were made to model the system under a variety of problematic, but realistic, conditions. (1) When one rate constant was seriously in error, adjustment of a different rate constant gave the greatest improvement in the model fit. (2) When a contaminant was present in the experiment, the effects could be hidden by the adjustment of the rate constants. (3) When an incorrect reaction mechanism was assumed, the error could be hidden by parameter adjustment if the concentrations of only one of the reacting species were considered or if an unweighted fit was used for the optimization. (4) Parameter values adjusted for one set of experimental conditions gave a poorer fit than did the unadjusted parameter values when attempting to model a new set of experimental condition (addition of an inhibitor). These results show the potential dangers of adjusting parameter values and the importance of measuring as many variables as possible in a complex system.

Animals↗
PubMed2004

A survey of mathematical models of competition with an inhibitor.

Mathematical models of the effect of inhibitors on microbial competition are surveyed. The term inhibitor is used in a broad sense and includes toxins, contaminants, allelopathic agents, etc. This includes both detoxification where the inhibitor is viewed as a pollutant and control where the inhibitor is viewed as an aid to controlling a bioreactor. The inhibitor may be supplied externally or may be created as an anti-competitor toxin. This includes plasmid-bearing, plasmid-free competition. The literature is spread across journals in different disciplines and with different notation. The survey attempts to present the mathematical models and the results of the corresponding analysis within a common framework and notation. Detailed mathematical proofs are not given but the methods of proof are indicated, references cited, and the results presented in tables. Open problems are indicated where there is a gap in the theory.

Bioreactors↗
PubMed1997

Mathematical modeling of biofilms.

A set of mathematical equations constitutes a mathematical model if it aims to represent a real system and is based on some theory of that system's operation. On this definition, mathematical models, some very simple, are everywhere in science. A complex system like a biofilm requires modeling by numerical methods and, because of inevitable uncertainties in its theoretical basis, may not be able to make precise predictions. Nevertheless, such models almost always give new insight into the mechanisms involved, and stimulate further investigation. The way in which diffusion coefficients are measured for use in a model, particularly whether they include effects of reversible reaction, is a key element in the modeling. Reasons are given for separating diffusion from reversible reaction effects and dealing with them in a separate subroutine of the model.

Bacterial Adhesion↗
PubMed2003

Mathematical models and their application in body composition research.

Mathematical models are a means of formalizing the knowledge on living systems obtained in clinical physiology and theoretical biophysics. They allow the actual processes in living systems to be described and the mechanisms of these systems to be evaluated. The study of body composition strives to quantitatively evaluate intrinsic body compartments and to obtain important information on the nutritional and energy requirements of healthy persons and those with various pathologies. Although there has been great progress in the development of sophisticated instruments for body composition research, it is not always possible to directly measure certain body compartments (e. g. intracellular water and fat mass) because of either technical difficulties or for ethical reasons. Therefore, mathematical models, which can potentially estimate these compartments indirectly, may be a viable alternative. In this paper, we describe the various advances in the use of mathematical models for body composition research.

Body Composition↗