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At least 127 records · Page 7Linked to original sources
PubMed1991

Mathematical model of antiviral immune response regulation. II. Mathematical formalization of the modelled processes. Imitation of acute course of hepatitis B.

The mathematical formalization of the conceptual model for antiviral immune response regulation described in the preceding report was carried out. The mathematical model is presented as a system of 30 ordinary nonlinear differential equations with delays. The algorithm for numerical integration of the mathematical model is based on Gear's methods of variable step and variable order. Initial conditions and parameters, as well as intervals of plausible values for them, were chosen for adaptation of the model for description of acute hepatitis B.

Acute Disease↗
PubMedDate not supplied

[The efficacy of universal vaccination against the hepatitis B virus. Simulation with a mathematical model].

We present a mathematical model of the hepatitis B virus (HBV) infection in a community. The main object is to analyze the effects of two different strategies of mass vaccination: newborns or adolescents. It appears that adolescents mass vaccination produces in the short-term a bigger effect than in the newborns. Mathematically, the model is a system of non linear first order differential equations, in which each function is a related class of individuals (susceptible, infectious, carrier, immune and death by HBV) in the evolution of the HBV. The solution of system is obtained in a numerical way. It should be pointed out that the model explains neatly the herd immunity effect of the vaccine and can be used in the simulation of possible changes in the HBV infection such that generalized use of discarded needles by the drug addicted population, changes in the sexual habits, etc.

Adolescent↗
PubMedDate not supplied

[Mathematical model of autoimmunity].

A mathematical model of autoimmunity is developed. This model is a system of two nonlinear differential equations, which describe the concentration dynamics of tissue cells and agressive lymphocytes. An analysis of the solutions shows that this model reproduces general behaviour of autoimmune diseases.

Autoimmune Diseases↗
PubMed1988

Quantitative assessment of cerebral blood flow using technetium-99m-hexamethyl-propyleneamine oxime: Part I, Design of a mathematical model.

To design a mathematical model for quantifying cerebral blood flow using 99mTc-hexamethyl-propyleneamine oxime (HM-PAO), basic studies were performed in animals and human volunteers. Microautoradiography revealed that HM-PAO crossed the blood-brain barrier. Thin layer chromatographic studies demonstrated the rapid disappearance of free HM-PAO in the brain tissue. Back diffusion from brain to blood was found negligible. From these observations, the familiar microsphere model was employed in the measurements of blood flow with HM-PAO. This, however, resulted in much lower flow values than simultaneously obtained values with the labeled microspheres. This underestimation was ascribed to the high affinity of HM-PAO to blood cells and serum protein. Taking the binding of HM-PAO to blood components into consideration, the following model equation was designed for quantifying cerebral blood flow: Ce(t) = Ca(t)-kCa(t)*exp(-kt), Cb(T) = F integral of T0 Ce(t)dt, where Ce and Ca are the free HM-PAO concentration in the intravascular space and the arterial whole-blood concentration of HM-PAO, respectively, as a function of time (t), Cb is the brain activity concentration, k is the rate constant for the binding of HM-PAO to the blood components, F is the blood flow value, T is time of measurement, and * denotes the operation of convolution. In clinical studies, Ca(t) and Cb(T) are obtainable from a dynamic single photon emission computerized tomographic study of the brain and multiple arterial blood sampling, respectively. The values for F and k can be estimated using a nonlinear least squares fitting method.

Animals↗
PubMed1999

Estimation of fetal weight in twins: a new mathematical model.

OBJECTIVES: Evaluation of new mathematical formula (Femur 4) derived from a twin population to estimate fetal weight in twins using ultrasound. Comparison of Femur 4 is with conventional mathematical models. DESIGN: Retrospective analysis of ultrasonic measurements of 297 twin babies from 24 to 40 weeks of gestation who were born within 10 days of ultrasound examination. SETTING: Aberdeen Maternity Hospital. METHODS: With ultrasonic measurements obtained from twin babies, estimated fetal weight was calculated using the mathematical models of Campbell, Shepard and Hadlock. The calculations were repeated for the model of Femur 4. All models were compared against Femur 4. RESULTS: The coefficient of determination of the linear regression between the actual and predicted weight was highest for Femur 4 (0.852). Femur 4 had the highest proportion of babies with estimated weights within 10% of actual birthweight (71.4%). In babies who weighed between 2000 and 3000 g, Femur 4 had the least systematic and random error of -1.69 and 8.96, respectively. For babies below the 10th centile for weight, Femur 4 had comparable positive and negative predictive values of 76.0% and 92.3%, respectively. Femur 4 was equally poor at predicting growth discordancy with positive and negative predictive values of 70.0% and 86.5% only. CONCLUSION: Femur 4 requires measurements of femur length and abdominal circumference only, hence avoiding the need to obtain difficult head measurements which is a common problem in twins. It is a good model for estimation of fetal weight in twins. However, prediction of growth discordancy remains problematic.

Body Weight↗
PubMed1988

Ventricular volume regulation: a mathematical model and computer simulation.

A mathematical model of ventricular volume regulation based on fluid mechanical principles has been constructed using a systems engineering approach. The parameters used in the model are based on clinical observation, laboratory investigation, and presumptions that will be tested later. The model was constructed to be the basis of a computer simulation. Using the computer simulation, information obtained from the literature and laboratory hypotheses regarding pathophysiology, several enigmatic conditions were tested. The model predicted that over-production of cerebrospinal fluid, as in the case of choroid plexus papilloma, could by itself lead to distention of the ventricular system. In simulating pseudotumor cerebri, if cerebrospinal fluid absorption at the arachnoid villi is impaired and the brain itself is rendered incompressible by swelling, intracranial pressure rises and ventricular volume diminishes. Conversely, in normal-pressure hydrocephalus, if cerebrospinal fluid flow is restricted between the spinal and cortical subarachnoid spaces and the brain is made more compressible, the ventricular volume increases with minimal increases in intracranial pressure. This mathematical model and its associated computer simulation is useful in predicting the behavior of the volume of the cerebral ventricles to a variety of pathological phenomena.

Animals↗
PubMed1984

Mathematical models for ligand-receptor binding. Real sites, ghost sites.

In the basic life sciences the term "model" implies a physical, chemical, or molecular construct that provides a representation for the interpretation of experimental observations. To the statistician, however, a model is a mathematical expression for correlating data, which may or may not have roots in a molecular picture. With regard to ligand-receptor interactions, the mathematical model used plays a crucial role in extrapolations of binding measurements. Regardless of the statistical goodness of fit of data to an equation, the relationships of the parameters of a mathematical formalism to the molecular features of ligand-receptor complexes are generally very complex. Oversimplified interpretations of the molecular significance of the constants derived from binding measurements are unwarranted, unless one has independent information from molecular probes.

Kinetics↗
PubMed2000

Brain biomechanics: mathematical modeling of hydrocephalus.

The considerable amount of literature on mathematical models of hydrocephalus and other brain abnormalities is critically reviewed. These models have various degrees of mathematical sophistication, and have influenced not only the diagnosis of hydrocephalus, but also its treatment with CSF shunts. The mathematical models are classified into two classes, pressure-volume models, and consolidation models. Advantages and disadvantages of both types are pointed out with a view to removing the confusion frequently generated by the technical aspects of the subject. The conclusion is reached that, while none of the current models are good enough to be of immediate use to the neurosurgeon, mathematical models are likely in the future to be a powerful tool for the understanding and the treatment of hydrocephalus, as well as other conditions related to brain biomechanics. The amount of mathematics has been kept to the absolute minimum, but it is cited and appended for those who would like to dig further into this fascinating area of research.

Biomechanical Phenomena↗
PubMedDate not supplied

[Mathematical modelling in medicine and biology. Theoretical basis and fundamentals].

Mathematical modelling is currently a common tool in the study of physiological and biochemical systems. Its basis and fundaments are not, however, well known by the non-specialist. Its aims are to describe, explain and predict physiological and biochemical phenomena. Mathematical models provide a concise and objective description of complex dynamic processes by defining, through mathematical equations, the relationships between quantitative measurements; they indicate, also, ways to improve experimental designs, and allow the testing of hypotheses about physiological or biochemical phenomena. Mathematical models can be developed from simple non-compartmental representations to large scale multi-compartmental models. The basic steps in the formulation of a model include conceptualization, realization and solution of the model. Each step has to be verified and validated. In the case of compartmental models, mass-balance equations are used to represent each compartment. A brief review of the theory of system's analysis and the general aims of mathematical modelling is presented here. The modelling process is usually started with a definition of the problem and a parameter identification followed by the setting up of a clear conceptual model of the system. The model consists of the description of the principal flows of material (in and out) and of the main components which store, convert or transmit these flows. A selection of the class of mathematical representation follows, i.e. linear or non-linear, in order to formulate the equations relating the input and output flows of material for each individual component of the system.(ABSTRACT TRUNCATED AT 250 WORDS)

Models, Biological↗
PubMed1992

Oncogenes, anti-oncogenes and the immune response to cancer: a mathematical model.

We develop a mathematical model for the initial growth of a tumour after a mutation in which either an oncogene is expressed or an anti-oncogene (i.e. tumour suppressor gene) is lost. Our model incorporates mitotic control by several biochemicals, with quite different regulatory characteristics, and we consider mutations affecting the cellular response to these control mechanisms. Our mathematical representation of these mutations reflects the current understanding of the roles of oncogenes and anti-oncogenes in controlling cell proliferation. Numerical solutions of our model, for biologically relevant parameter values, show that the different types of mutations have quite different effects. Mutations affecting the cell response to chemical regulators, or resulting in autonomy from such regulators, cause an advancing wave of tumour cells and a receding wave of normal cells. By contrast, mutations affecting the production of a mitotic regulator cause a slow localized increase in the numbers of both normal and mutant cells. We extend our model to investigate the possible effects of an immune response to cancer by including a first order removal of mutant cells. When this removal rate exceeds a critical value, the immune system can suppress tumour growth; we derive an expression for this critical value as a function of the parameters characterizing the mutation. Our results suggest that the effectiveness of the immune response after an oncogenic mutation depends crucially on the way in which the mutation affects the biochemical control of cell division.

Animals↗
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↗
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↗