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Results for “Mathematical Model”

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At least 235 records · Page 13Linked to original sources

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↗

PubMed2005

A mathematical model for tear drainage through the canaliculi.

PURPOSE: Tear drainage through the canaliculi has been extensively studied experimentally but there has been no attempt to develop a quantitative model for this process. In this paper, we develop a mathematical model for the tear drainage through the canaliculi. METHODS: The mathematical model is based on the experimental findings of Doane, according to which the muscle action during a blink drives the tear drainage. In this paper, mathematical models are developed for the tear flow and the canalicular deformation, and the model equations are solved to predict the tear drainage rates. RESULTS: The drainage rates depend on various physiological parameters. The time to attain a steady state during the drainage process can vary from about 0.0010 s to 0.0546 s, and the tear drainage rate can vary from 0.10 microl/min to 4.00 microl/min for a normal tear film, for physiologically reasonable values of various system parameters. CONCLUSIONS: The model predictions agree with various physiological experiments, at least qualitatively. The model also helps resolve the differences between various tear drainage experiments.

Blinking↗

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↗

PubMed2007

Flow-dependent transport in a mathematical model of rat proximal tubule.

The mathematical model of rat proximal tubule has been extended to include calculation of microvillous torque and to incorporate torque-dependent solute transport in a compliant tubule. The torque calculation follows that of Du Z, Yan Q, Duan Y, Weinbaum S, Weinstein AM, and Wang T (Am J Physiol 290: F289-F296, 2006). In the model calculations, torque-dependent scaling of luminal membrane transporter density [either as an ensemble or just type 3 Na(+)/H(+) exchanger (NHE3) alone] had a relatively small impact on overall Na(+) reabsorption and could produce a lethal derangement of cell volume; coordinated regulation of luminal and peritubular transporters was required to represent the overall impact of luminal flow on Na(+) reabsorption. When the magnitude of torque-dependent Na(+) reabsorption in the model agrees with that observed in mouse proximal tubules, the model tubule shows nearly perfect perfusion-absorption balance at high luminal perfusion rates, but enhanced sensitivity of reabsorption at low flow. With a slightly lower coefficient for torque-sensitive transporter insertion, perfusion-absorption balance in the model tubule is closer to observations in the rat over a broader range of inlet flows. In simulation of hyperglycemia, torque-dependent transport attenuated the diuretic effect and brought the model tubule into closer agreement with experimental observation in the rat. The model was also extended to represent finite rates of hydration and dehydration of CO(2) and H(2)CO(3). With carbonic anhydrase inhibition, torque-dependent transport blunted the diuretic effect and enhanced the shift from paracellular to transcellular NaCl reabsorption. The new features of this model tubule are an important step toward simulation of glomerulotubular balance.

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

[A mathematical model of electrosurgical endoscopical polypectomy].

A mathematical model of electrosurgical polypectomy was suggested. The problem of emitted heat distribution in biological tissues exposed to endosurgical loop electrode was solved. Analysis of the obtained solution made it possible to determine the dependence of the results of electrosurgery on the parameters of the loop electrode and the loop size. Optimization of load performance allowed the efficiency of electrosurgical polypectomy to be increased.

Electricity↗

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↗

PubMed2005

Cost-effective G-CSF therapy strategies for cyclical neutropenia: mathematical modelling based hypotheses.

Using computer simulations of a mathematical model for the regulation of stem cell and neutrophil production in dogs, we have studied the efficacy of four different treatment protocols for cyclical neutropenia involving granulocyte colony stimulating factor (G-CSF). The first treatment scheme is based on the bifurcation analysis of the mathematical model and proposes a daily, phase-dependent, protocol. The second involves alternate day administration of G-CSF. The third triggers G-CSF administration whenever neutrophil levels fall below a predetermined level, and the fourth one follows a random administration protocol. The computer simulations predict that clinically desirable results can be achieved with the three last methods, using far less G-CSF than would be needed with the standard daily treatment. If the results of this modelling are borne out clinically, they will entail a considerable financial savings for patients.

Animals↗

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↗