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PubMed1981

A mathematical model for analysing cellular age-response functions in terms of physiological age.

A mathematical model is presented which facilitates the analysis of cellular age-response functions in terms of the physiological ages of the cells. Age-response functions are generally determined by obtaining synchronous cohorts of cells and measuring the sensitivity of the cohorts to the treatment agent at different times after selection (i.e., several different chronological ages). The model described here uses data on the [3H]TdR labelling patterns of the cell population to determine the distribution of physiological ages for the cohorts at the times of treatment. The age-response function data are then analysed in terms of the physiological ages of the cells. The compartments used in the analysis may be chosen according to the biology of the system and the wishes of the experimenters and not imposed by the variability of the phase durations. The application of the model is illustrated using the age-response functions for EMT6 cells exposed to radiation and HeLa cells exposed to hydroxyurea.

Animals↗
PubMed2003

A mathematical model accounting for the organization in multiplets of the genetic code.

A model using suitable mathematical operators in the crystal basis model of the genetic code is presented. This model retains a requirement for stability of the genetic code against misreading or translation errors. The main features (including number of encoded amino-acids, nucleotide content, and synonymous codons multiplet dimension) are described for mitochondrial and eukaryotic genetic codes.

Genetic Code↗
PubMed1998

Use of a mathematical model to evaluate breast cancer screening policy.

A model of breast cancer screening was developed, in which the processes of tumour origination and growth, detection of tumours at screening, presentation of women with cancers to their GP, and of survival after diagnosis were modelled parametrically. The model was fitted to data from the North-West of the UK, for 413 women who screened positive, and for 761 women who developed interval cancers. Model validation comprised verification that the final model fitted the data adequately, together with the comparison of model predictions with findings by other workers. The mathematical model was used to assess different screening policies, and to ask "what if" questions. Taking the cost of breast cancer to be the sum of the cost of screening and the cost of PYLL (person years of life lost due to cancer), the optimal screening policy was calculated. The costs of the current policy and of other possible screening policies were found, together with their effects on life lost and on mortality. The tentative conclusion was that if monies can be found to extend the screening programme, for example to carry out one more screen per woman, most benefit would be obtained by reducing the start age of screening by 3 years.

Aged↗
PubMedDate not supplied

A mathematical model and CD4+ lymphocyte dynamics in HIV infection.

The paper presents a model of CD4 + lymphocyte dynamics in HIV-infected persons. The model incorporates a feedback mechanism regulating the production of T lymphocytes and simulates the dynamics of CD8 + lymphocytes, whose production is assumed to be closely linked to that of CD4 + cells. Because CD4 + lymphocyte counts are a good prognostic indicator of HIV infection, the model was used to simulate such therapeutic interventions as chemotherapy and active and passive immunization. The model also simulated the therapeutic administration of anti-CD8 antibodies; this intervention was assumed to activate T-cell production by activating a feedback mechanism blocked by the high numbers of CD8 + lymphocytes present in HIV-infected persons. The character and implications of the model are discussed in the context of other mathematical models used in HIV infection.

CD4 Lymphocyte Count↗
PubMed1997

Study of mathematical model for product formation with recombinant microbes expressed IFN.

Based on the known molecular interactions of aporepressor, corepressor, and inducer, a mathematical model of product formation about the Trp operon regulated recombinant microbes has been proposed. The linear relation of the overall transcription rate constant and overall translation rate constant on the specific growth rate has been suggested. We used experimental data where engineered microorganisms express interferon (IFN). Decay constant of IFN, mRNA transcription rate constant, and IFN expression rate constant have been estimated. An equation related to IFN concentration in fermentation on specific growth rate and Trp concentration has been obtained. By application of the equation, the expression of IFN is calculated based on Trp concentration and specific growth rate in fermentation. Also, the optimum overall culture time can be determined.

Escherichia coli↗
PubMed1979

Mathematical models of cancer and their use in risk assessment.

Cancer risk assessment necessarily involves the use of mathematical models. Although risk estimates can be extremely sensitive to underlying assumptions in such models, the assumptions are frequently overlooked when a particular model is used. This paper presents four examples to illustrate how the alteration of assumptions can have a large effect on risk estimates. Ways of avoiding undue model dependence are discussed.

Age Factors↗
PubMed2005

Assessment of Cottle's areas through the application of a mathematical model deriving from acoustic rhinometry and rhinomanometric data.

OBJECTIVES: Each nasal area, as defined by Cottle, has a different influence on the nasal airflow. The longitudinal distribution of resistances in nasal cavities was calculated by the anterior rhinomanometry and acoustic rhinometry data. DESIGN: Dynamic study of Cottle's areas in normal subjects was carried out by rhinomanometry and acoustic rhinometry. SETTING: Study by the Department of Otolaryngology of the University of Rome-La Sapienza. PARTICIPANTS: Twenty-seven Caucasian adults in local and general healthy conditions took part and completed this study, with a total of 54 nasal cavities included because of negativity at ENT-examination and clinical history, with normal respiratory parameters at the rhinomanometry and acoustic rhinometry. MAIN OUTCOME MEASURES: We determined nasal and acoustic resistances, nasal volumes and cross-sectional surface areas, as defined by Cottle, using nasal endoscopy. The longitudinal distribution of nasal resistances was obtained by integrating experimental surface areas using a novel mathematical model. The estimation of the longitudinal nasal resistance variations as a result of a theoretical reduction of the surface areas. RESULTS: The reduction of the 2-3-1 areas (in this order of importance) showed the greatest influence on the nasal resistances with coefficients of determinations greater than 0.98, this being quite different from that of the areas 4 and 5 for quite smaller area reduction percentages. CONCLUSIONS: The areas 2-3-1 control the overall nasal resistance so the surgical procedures on these areas greatly influence the dynamics of nasal airflow. The mathematical model developed here gives useful information to nasal functional surgery and may be applied to other schemes of nasal cavity.

Acoustics↗
PubMed1998

A mathematical model for Neanderthal extinction.

A simple mathematical homogeneous model of competition is used to describe Neanderthal extinction in Europe. It considers two interacting species, Neanderthals and Early Modern Men, in the same ecological niche. Using paleontological data we claim that the parameter of similarity, between both species, fluctuates between 0.992 and 0.997. An extension of the model including migration (diffusion) is also discussed; nevertheless, extinction of Neanderthal seems unavoidable. Numerical analysis of travelling wave solutions (fronts) confirms the extinction. The wave-front-velocity is estimated from linear analysis and numerical simulations confirm this estimation. We conjecture a mathematical formulation for the principle of exclusion between competitive interacting species (Gause).

Animals↗
PubMed1984

Mathematical model of biliary lipid secretion: a quantitative analysis of physiological and biochemical data from man and other species.

We propose a simple mathematical model to account for the coupling of secretion rates of bile salts, lecithin, and cholesterol into bile. The model assumes that: 1) molecules of "biliary" lecithin and cholesterol enter a functional compartment located in the endoplasmic reticulum of the hepatocyte from which they are secreted into bile, and in the case of cholesterol, also catabolized to bile salts; 2) the rates at which lecithin and cholesterol enter the "secretory" compartment are regulated independently by feedback loops that control their synthesis and/or uptake; 3) lecithin secretion is coupled by an unknown transport mechanism, possibly micellar or vesicular, to the flux of bile salts passing through the compartment; 4) cholesterol secretion is coupled by a similar mechanism to lecithin secretion and not to bile salt secretion directly; and 5) bile salt synthesis is proportional to the cholesterol content of the compartment. The model predicts that in the steady state the dependences, lecithin secretion vs bile salt secretion; cholesterol secretion vs lecithin secretion; and cholesterol secretion vs bile salt secretion, will all have the form of rectangular hyperbolae. Four independent parameters related to the postulated mechanisms of biliary lipid synthesis, uptake, and transport determine the quantitative features of these hyperbolae. These four "secretion parameters" also determine how the biliary lipid composition of hepatic and "fasting" gallbladder bile varies with bile salt secretion rate. A quantitative analysis of biochemical and physiological data on biliary lipid secretion in rat, dog, and man confirms the general predictions of the model. Deductions of the secretion parameters are made for each species and are compared with other relevant data on biliary lipid metabolism. From this analysis, we offer new insights into: i) the species differences in biliary lipid secretion and bile composition; ii) the influence of obesity on biliary lipid secretion in man; and iii) the causes of cholesterol super-saturation in fasting gallbladder bile.

Animals↗
PubMed1978

[Mathematical model of the propagation of a vulpine rabies epizootic (author's transl)].

A mathematical model of propagation of a vulpine rabies epizootic has been worked out in order to build a prediction tool and to fix a suitable prophylaxis. The main ecological hypotheses and their mathematical expression are presented. This consists of a system of two integro-differential equations which have been discretizited to approximate their solution numerically. The results of the simulation of this model are consistent with the data observed in the field.

Animals↗
PubMedDate not supplied

[A mathematical model of the behavior formation in mastering the determinate patterns of stimuli].

The paper deals with studying and with analyzing a variety of mathematical models designed for constructing the behavior under the conditions of mastering the determinate patterns of stimuli. Models of random reaction choice and of random strategy choice are viewed as basic ones. A two-parameter model designed for shaping a strategy choice was investigated and suggested. The model describes a strategy choice on the basis of commemorating the previous experience with regard for an intensity of forgetting the mastered experience and on the basis of an independent and spontaneous shaping of patterns. The model was used to interpret the changes, observed in the behavioral indices of patients with schizophrenia and oligophrenia versus the virtually healthy subjects, as changes of actualization of applying the previously mastered experience and those of the forgetting speed up.

Adolescent↗
PubMed1985

A comparison of sheep and human fetal oxygen delivery systems with use of a mathematical model.

Human fetal cardiac output measured with ultrasound is only about 60% of that found in the sheep. We modified a previously developed mathematical model of the fetal circulation and oxygen delivery in sheep for the human in order to study several differences. The model predicts that a human fetus can maintain its oxygen delivery with a relatively low cardiac output because of its relatively high fetal hemoglobin concentration, as compared with that of the sheep fetus. Thus an inverse relationship between fetal hemoglobin concentration and fetal cardiac output is suggested. This relationship may be mediated by the influence of red blood cell concentration on blood viscosity. Furthermore, it indicates that fetal anemia should be detectable by ultrasound measurements of increased cardiac output and/or umbilical blood flow. Dynamic responses of the model suggest that the mechanism of late and variable decelerations in the fetal heart rate pattern is mediated via a fall in arterial oxygen tension.

Animals↗
PubMed2004

Estimation of parameters for a mathematical model of growth hormone secretion.

Here, we describe partial calibration of a parsimonious mathematical model of growth hormone (GH) secretion. From first principles, we derived a model of the effects on GH secretion from pituitary somatotrophs of stimulation by GH-releasing factor (GRF) or GH secretagogue, and of inhibition by somatostatin. We obtained a concise model by collapsing the many processes of the signal transduction cascade into a single step broadly reflecting the initial binding of GRF to its receptors. In the model, GH secretion is proportional to the rate of binding of GRF to activatable receptors. Desensitization occurs because of reduction of free receptors/available effector units, and resensitization occurs as those lost are replaced. This replacement is speeded up in the presence of somatostatin, which also inhibits GH secretion by reducing the constant of proportionality between the rate of GH secretion and the rate of GRF binding. We derived simple mathematical equations for the rate of GH secretion and cumulative secretion. Using these, we tested the model against data obtained from experiments performed in vitro, and made it quantitative using rigorous statistical approaches to optimize parameter estimates. The behaviour of the calibrated model matches experimental observations closely.

Algorithms↗
PubMed2003

Direct comparison of calculated hip joint contact forces with those measured using instrumented implants. An evaluation of a three-dimensional mathematical model of the lower limb.

Characterisation of hip joint contact forces is essential for the definition of hip joint prosthesis design requirements. In vivo hip joint contact force measurements have been made using instrumented hip joint prostheses. However, to allow determination of the range of values of joint contact force and their directions relative to anatomical structures in a range of subject groups sufficient to form an agreed data base it is necessary to adopt a different approach without the use of an implanted transducer. The use of mathematical models of the lower limb to examine the forces in soft tissues and at the joints has provided valuable insight into internal loading conditions. Several authors have proposed mathematical musculo-skeletal models. However, there have been only limited attempts at validation of these models. It is possible to use the results of in vivo force measurements from instrumented prostheses to validate the results calculated using the mathematical models. In this study two subjects with instrumented hip joint prostheses were studied. Forces at the hip joints were calculated using a three-dimensional model of the leg. Walking at slow, normal and fast speeds (0.97-2.01m/s), weight transfer from two to one leg and back again, and sit to stand were studied. Direct comparisons were made between the 'gold standard' measured hip joint contact forces and the calculated forces. There was general agreement between the calculated and measured forces in both pattern and magnitude. There were, however, discrepancies. Reasons for these differences in results are discussed and possible model developments suggested.

Computer Simulation↗
PubMed1992

Mathematical modelling of microenvironment and growth in EMT6/Ro multicellular tumour spheroids.

In order to determine the role of micromilieu in tumour spheroid growth, a mathematical model was developed to predict EMT6/Ro spheroid growth and microenvironment based upon numerical solution of the diffusion/reaction equation for oxygen, glucose, lactate ion, carbon dioxide, bicarbonate ion, chlorine ion and hydrogen ion along with the equation of electroneutrality. This model takes into account the effects of oxygen concentration, glucose concentration and extracellular pH on cell growth and metabolism. Since independent measurements of EMT6/Ro single cell growth and metabolic rates, spheroid diffusion constants, and spinner flask mass transfer coefficients are available, model predictions using these parameters were compared with published data on EMT6/Ro spheroid growth and micro-environment. The model predictions of reduced spheroid growth due to reduced cell growth rates and cell shedding fit experimental spheroid growth data below 700 microns, but overestimated the spheroid growth rate at larger diameters. Predicted viable rim thicknesses based on predicted near zero glucose concentrations fit published viable rim thickness data for 1000 microns spheroids grown at medium glucose concentrations of 5.5 mM or less. However, the model did not accurately predict the onset of necrosis. Moreover, the model could not predict the observed decreases in oxygen and glucose metabolism seen in spheroids with time, nor could it predict the observed growth plateau. This suggests that other unknown factors, such as inhibitors or cell-cell contact effects, must also be important in affecting spheroid growth and cellular metabolism.

Animals↗
PubMedDate not supplied

[Mathematical modeling of the kinematic reaction of the human body to impact accelerations].

This paper considers the problem of selecting the structure of a mathematical model that describes the kinematic reactions of the human body during traffic accidents. The paper presents a calculation procedure and a program that allow selection of a structure (up to 17 elements) without deriving repeatedly equations of motion as well as automatic recalculation of all inertia and size parameters.

Acceleration↗
PubMedDate not supplied

Approximate formulae (deduced from a mathematical model) for the characteristics of the interepidemic and epidemic periods of some virus diseases.

By a qualitative analysis of the solutions of the mathematical model equations (describing the morbidity and susceptibility evolution in a viral epidemics), approximate formulae for the extreme values of the variables and for the duration of the main phases of a multiannual cycle are deduced. These formulae were validated by numerical simulation of the solutions, leading to the exact values of the mentioned essential characteristics of the diseases propagation.

Disease Outbreaks↗