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At least 199 records · Page 11Linked to original sources
PubMed2002

Mathematical models of human CD4+ T-cell population kinetics.

We review how mathematical models help the interpretation of data measuring CD4+ T-cell kinetics by two recently-developed techniques. Mathematical models are developed for the average content of T-cell receptor excision circles (TRECs) and the average telomeric restriction fragment (TRF) in T-cells in the peripheral blood. Changes in the TRECs were supposed to indicate changes in thymic production. The rate at which naive and memory CD4+ T-cells erode their telomeres was supposed to reflect their respective division rates. Analysing the mathematical models, we show that rapid changes in the TRECs per naive T-cell are most likely due to changes in the division rates, and that the rates of telomere erosion fail to reflect naive and memory division rates. The model is applied to explain data showing that rheumatoid arthritis (RA) patients have abnormal TRECs and telomeres.

Arthritis, Rheumatoid↗
PubMed1991

Mathematical modelling of flow through an irregular arterial stenosis.

A mathematical model of flow through an irregular arterial stenosis is developed. The model is two-dimensional and axi-symmetric with the stenosis outline obtained from a three-dimensional casting of a mildly stenosed artery. Agreement between modelled and experimental pressure drops (obtained from an axi-symmetric machined stenosis with the same profile) is excellent. Results are also obtained for a smooth stenosis model, similar to that used for most mathematical modelling studies. This model overestimates the pressure drop across the stenosis, as well as the wall shear stress and separation Reynolds number. Also, the smooth model predicts one instead of three recirculation zones present in the irregular model. The original stenosis is modified to increase the severity from 48 and 87% areal occlusion, while maintaining the same general shape. This has the effect of increasing the pressure drop by an order of magnitude and decreasing the number of recirculation zones to one, with a lower separation Reynolds number.

Arterial Occlusive Diseases↗
PubMed1994

A study of the singularities in a mathematical model for circadian rhythms.

One of the models that has been suggested for describing circadian rhythms mathematically is an extension of the van der Pol equation given by ÿ + 0.5(y2 + y-2 - 3)y + (1 + 0.6 y) y = z + z + z, where y is the oscillating variable, and z is the light intensity assumed to excite the oscillator. In order for the equation to exhibit self-sustained oscillations, z has to be within the oscillatory range (0.847 < z < 3.189). This equation has been shown to simulate several of the features possessed by circadian systems (Wever, R., 1984, Toward a mathematical model of circadian rhythmicity, in: Mathematical Models of the Circadian Sleep-Wake Cycle, M.C. Moore-Ede and C.A. Czeisler (eds.) (Raven Press, New York) pp. 17-79). Physiological experiments have been performed which show that circadian rhythms can have stable singularities. Therefore, it was of interest to investigate whether or not the equation given above also has this property. We have studied the stability of the two singularities of the model system above. One of the singularities is unstable and corresponds to non-physiological conditions. The other one is an unstable spiral point if the light conditions are such that oscillations can occur in the system. We conclude that the model mentioned above is unsuitable to describe circadian systems which have stable singularities. The model has been simulated, and pulses have been applied to the system by temporarily changing the value of z to find appropriate conditions forcing the system into its singularity. The strategy to find such pulses is discussed.

Animals↗
PubMedDate not supplied

[Mathematical modeling and optimization of plasmadiafiltration].

A mathematical model of mass transport of toxic substances with small, middle and large molecules weight in the body compartments and in the extracorporal system was worked out and used in the clinic for individual optimization and prediction of final results when treating patients with acute hepatic and renal failure in plasmadiafiltration. Permeability and the sieving coefficients were found "in vivo" in the plasma for 3 types of dialysers with different membranes. For practical use of this model a program was written by an interactive dialogue for the personal computer.

Acute Kidney Injury↗
PubMed2002

A mathematical model of metabolic insulin signaling pathways.

We develop a mathematical model that explicitly represents many of the known signaling components mediating translocation of the insulin-responsive glucose transporter GLUT4 to gain insight into the complexities of metabolic insulin signaling pathways. A novel mechanistic model of postreceptor events including phosphorylation of insulin receptor substrate-1, activation of phosphatidylinositol 3-kinase, and subsequent activation of downstream kinases Akt and protein kinase C-zeta is coupled with previously validated subsystem models of insulin receptor binding, receptor recycling, and GLUT4 translocation. A system of differential equations is defined by the structure of the model. Rate constants and model parameters are constrained by published experimental data. Model simulations of insulin dose-response experiments agree with published experimental data and also generate expected qualitative behaviors such as sequential signal amplification and increased sensitivity of downstream components. We examined the consequences of incorporating feedback pathways as well as representing pathological conditions, such as increased levels of protein tyrosine phosphatases, to illustrate the utility of our model for exploring molecular mechanisms. We conclude that mathematical modeling of signal transduction pathways is a useful approach for gaining insight into the complexities of metabolic insulin signaling.

Animals↗
PubMed1986

A mathematical model of the patellofemoral joint.

A mathematical model of the patellofemoral joint taking into account movements and forces in the sagittal plane is described. The system parameters of the model are the locations of the attachments of the quadriceps muscle and the patellar ligament, the length of the patellar ligament, the dimensions of the patella and the geometry of the articulating surfaces. They were obtained from ten autopsy knees. The model enables calculation of the relative position of the patella, patellar ligament and quadriceps tendon, the location of the patellofemoral contact point and the magnitude of the patellofemoral compression force and the force in the patellar ligament as a function of the location of the tibial tuberosity at different flexion-extension angles of the knee. The model is validated by comparing model data with experimentally determined data.

Biomechanical Phenomena↗
PubMed1997

The S factor--a new derived hemodynamic oxygenation parameter--a useful tool for simplified mathematical modeling of global problems of oxygen transport.

We describe a new derived hemodynamic oxygenation parameter, the S factor (S). The factor is based on oxygen delivery and oxygen consumption and can range from -3 to 1. It allows simplified mathematical modeling of clinical problems of oxygen transport and can be applied to many clinical situations. A new hemodynamic oxygenation parameter, the S factor (S), is introduced as an aid to mathematical modeling. It is defined as follows: [formula: see text] (DO2 = oxygen delivery, VO2 = oxygen consumption) S can theoretically vary from -3 (DO2 = VO2) to +1 (VO2 = 0). When DO2/VO2 = 4 (ie. OER = 0.25), S = 0. An S < 0 implies utilization of reserve oxygen transport capacity. An S > 0 implies increased oxygen delivery in relation to oxygen consumption (ie. "shunted oxygen delivery"). By algebraic manipulation and substitution of the components of DO2 into Equation 1: DO2 = Q x Ca x 10 DO2 = Q [(Hb)(Sat)(1.36) + PaO2(.0031)] 10 (2) the following equations can be derived: [formula: see text] [formula: see text] Ca - Cv (Ca = arterial content, Cv = venous content) can be determined by substituting components of oxygen consumption: VO2 = Q (Ca - Cv) x 10 (5) into equation 1 and solving for Ca - Cv. [formula: see text] Equation 6 can be simplified to: [formula: see text] A previously defined relationship between mixed venous PO2 (PvO2) and DO2/VO2 (where calculated P50 is 26.6 +/- 1.0) can be used to modify S in a clinically relevant manner. PvO2 = 5.44D O2/VO2 + 18.16 (8) The relationship between S and PvO2 can be defined by substituting Equation 4 into Equation 1 and solving for PvO2 PvO2 = [21.76/(1-S)] + 18.16 (9) As an example, at a PvO2 of 28 torr (anaerobic threshold), S = -1.2. The relationship between PvO2 and S is shown in Figure 1. S, which can also be defined as 1-4(VO2/DO2) or 1-4(OER), is a useful tool for mathematical modeling of global problems of oxygen transport because the previously derived equations with the S value allow the components of oxygen transport to be interrelated in a clinically relevant manner. Additional advantages of using S in mathematical modeling are: 1. Conceptually it 'fits' in that in regards to the sign (+ or -), as a -S implies utilization of reserve oxygen transport capacity and a +S implies wasted or excess oxygen delivery (shunted). 2. These concepts are easily quantified using the S factor. 3. It 'spreads out' the difference between values for parameters (OER or S) integrating components of oxygen transport, ie. in the 'normal state' regarding oxygen transport, OER = 0.25 and S = 0. At the anaerobic threshold (PvO2 = 28 torr), OER = 0.55 and S = -1.2. Thus, the change in OER from 'normal state' to anaerobic threshold is 0.3 (0.55-0.25) and the change in S is 1.2. This represents a four-fold increase. Four examples of mathematical modeling of global problems of oxygen transport using the S factor are described below.

Anaerobiosis↗
PubMed2002

Mathematical models of HIV pathogenesis and treatment.

We review mathematical models of HIV dynamics, disease progression, and therapy. We start by introducing a basic model of virus infection and demonstrate how it was used to study HIV dynamics and to measure crucial parameters that lead to a new understanding of the disease process. We discuss the diversity threshold model as an example of the general principle that virus evolution can drive disease progression and the destruction of the immune system. Finally, we show how mathematical models can be used to understand correlates of long-term immunological control of HIV, and to design therapy regimes that convert a progressing patient into a state of long-term non-progression.

Algorithms↗
PubMed1996

Mathematical models of transmission dynamics and control of schistosomiasis.

Mathematical models are potentially valuable aids to a quantitative understanding of schistosome epidemiology and to the design of control programs. A basic theoretical framework is described that is developed to incorporate the impact of acquired immunity, heterogeneous transmission rates, and the effects of control measures. Models that assume that acquired immunity acts to moderate the rate of human infection make predictions consistent with age-intensity data from different human populations. Models incorporating heterogeneous water contact behavior can be applied to suitable field data and used to predict the potential efficacy of targeted chemotherapy or focal molluscicide application. More complex and detailed models can be used in simulation studies to assist with the design of field trials and in the interpretation of data from these trials. These applications of mathematical models suggest several areas requiring further theoretical development and also indicate areas in which adequate field data are still lacking.

Animals↗
PubMedDate not supplied

[The mathematical modelling of tropical malaria].

The new mathematical model of P. falciparum malaria has been created. One means the operational forecast of epidemic process when different control measures are realized. The original modelling methodology for epidemics is used. The proposed methodology is allowed to take into account the natural variety of model's parameters. The malaria model consists of the nonlinear integro-differential in partial derivatives combined equations including individual and population characteristics. The informatics technologies permits to see information about model and its grounds. The model's verification has been done on data of Garki-project.

Disease Outbreaks↗
PubMed1987

Antigenic relationships between avian paramyxoviruses. II. A combinatorial mathematical model of antigenic kinship.

A combinatorial mathematical model describing the antigenic relationships found between different avian paramyxovirus (PMV) serotypes (Lipkind and Shihmanter, 1986) is presented. According to the model, the network of the antigenic interconnections is determined by the specific combinatorial sets of antigenic determinants, some of them being serotype-specific and the others being common to certain other avian PMV serotypes. The suggested model is based on certain postulates concerning PMV virion structure; the bifunctional organization of PMV haemagglutinin-neuraminidase (HN) glycoprotein, its amount per virion and a mechanism of antibody-caused inhibition of its functional activities; the definition of an antigenic determinant as an elementary unit inducing and reacting only with a homologous type of antibodies. The model interprets in specific terms some serological results, in particular the old but mysterious phenomenon of asymmetric cross reactivity.

Animals↗
PubMed1993

Fetal growth: a comparison of growth curves with mathematical modeling.

This study compared the use of fetal growth curves with the Rossavik mathematical model in predicting third trimester fetal growth in 27 Hispanic patients. The parameters tested were BPD, HC, AC, and FL. The growth curve method of predicting third trimester fetal growth was significantly more accurate than the mathematical model for three of the four fetal parameters tested: BPD, HC, and FL. We conclude that the mathematical model method offered no advantage over the more commonly used growth curve method for predicting third trimester fetal growth. In addition, growth curves do not require complex calculations and are conceptually simpler and easier to use.

Adult↗
PubMed2002

Mathematical modeling in glucose metabolism and insulin secretion.

PURPOSE OF REVIEW: Mathematical models in the study of glucose metabolism, insulin secretion and the insulin-glucose interactions have a longstanding tradition. The recent advances in this area are reviewed, with particular emphasis on the methods for the assessment of insulin sensitivity and insulin secretion. The available models are illustrated, and their common aspects and differences discussed. RECENT FINDINGS: For the assessment of insulin sensitivity and beta-cell function, several modeling methods have recently been developed. Models for insulin sensitivity provide insulin-sensitivity indices from simple clinical tests, or a rich multiple-parameter characterization of insulin sensitivity from more elaborate experiments. Models for beta-cell function yield indices that quantify the ability of the beta-cells to respond to glucose stimuli. Furthermore, models of the insulin-glucose interactions propose interesting explanations of some experimental observations such as insulin-glucose oscillations and the progression to type 2 diabetes. SUMMARY: Mathematical models in this area continue to evolve toward more accurate and clinically applicable approaches, and should be considered as a useful resource for clinical investigators. Models also have a potentially important role for understanding the mechanisms governing the insulin-glucose regulation system.

Animals↗
PubMed1988

Mathematical models to predict behaviour of tumours?

Mathematical modeling is an important tool in science that allows the investigator to examine phenomena that are not easily studied by direct experiment. The growth of neoplasms and their response to treatment are processes that appear particularly well suited for study by this approach. The ready availability of inexpensive powerful microcomputers and sophisticated software makes this research avenue open to all experimental and clinical oncologists.

Drug Resistance↗
PubMedDate not supplied

[Description of electromyograms using a mathematical model of single joint movement].

A mathematical model for motor control over one-joint fast and slow movements is proposed based on the equilibrium point (EP) hypothesis. Equations describing a reaction of the muscle with its servo to an EP shift are presented. EMG level is estimated as a function of kinematic and control variables. Voluntary movements are performed by a ramp EP shift for the muscles subserving a given joint. EMG patterns obtained by a computer simulation are in good agreement with the experimental data.

Biomechanical Phenomena↗
PubMed1980

[Choice of the association model of rabbit muscle phosphofructokinase using mathematical modeling].

The sedimentation behaviour of the subform of rabbit muscle phosphofructokinase specifically eluted from DEAE cellulose by citrate was studied in different media by velocity experiments. The measured sedimentation coefficients of different components in the system can be classified into 12 groups, which is indicative of a complex multistep association process of the enzyme (with more than 3 oligomers). The concentration dependence of weight average sedimentation coefficient of phosphofructokinase was a studied. The choice of the probable association model of phosphofructokinase oligomers at low protein concentration was accomplished by means of computer simulation of the association process. Of 26 closed association models tested 14 models with 2 or 3 association constants are indistinguishable in view of Student's t-criterion of significance. All uniparametric association models studied significantly inferior approximate the experimental data. It is supposed that the dimer is not the structural unit of polymerization. Having this in mind and taking into account the demand for the multistep process, one may consider as most probable only 8 models of phosphofructokinase association, namely monomer-dimer-trimer-tetramer-monomer-dimer-tetramer-octamer (with 3 association constants) and linear polymerization up to the octamer with 2 association constants, where the "monomer" of association may be defined as trimer, tetramer or hexamer of subunits.

Animals↗
PubMed1977

A mathematical model of a blood-gas service.

A mathematical model depicting operation of a blood-gas workstation was developed by two systems analysts working closely with two clinical pathologists. This model was used to provide estimates of average as well as maximum turnaround times under various conditions of workload, specimen types (capillary vs. syringe), methodology (use of IL 513 vs. IL 313 for capillary samples), and reporting procedures (report each sample as analyzed vs. report after analysis of all samples in batch). These estimates have been validated against actual experience in our laboratory. Such an objective mathematical model can be used to plan optimal service.

Blood Gas Analysis↗
PubMed1987

The frequency of cervical cancer screening. Comparison of a mathematical model with empirical data.

The results of a mathematical model used to analyze the frequency of the Pap smear are compared with a recently published independent empirical study of data from large screening programs in Europe and North America. The model's predictions of the reduced incidence of invasive cervical cancer achieved with different screening frequencies match the empirical results closely--the predictions were within 1% of the empirical results for screening frequencies ranging from 1 to 10 years. The data indicate that compared with annual screening, screening every 2, 3, 5, and 10 years retains 99%, 97%, 89%, and 69%, respectively, of the effectiveness measured as a reduction in frequency of invasive cancer. The mathematical model underestimated the effectiveness of screening every 3 years, compared with screening every year.

Europe↗