Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Mathematical Model”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 937 records · Page 52Linked to original sources
PubMed2003

VO2, VCO2, and RQ in a respiratory chamber: accurate estimation based on a new mathematical model using the Kalman-Bucy method.

A respiratory chamber is used for monitoring O(2) consumption (Vo(2)), CO(2) production (Vco(2)), and respiratory quotient (RQ) in humans, enabling long term (24-h) observation under free-living conditions. Computation of Vo(2) and Vco(2) is currently done by inversion of a mass balance equation, with no consideration of measurement errors and other uncertainties. To improve the accuracy of the results, a new mathematical model is suggested in the present study explicitly accounting for the presence of such uncertainties and error sources and enabling the use of optimal filtering methods. Experiments have been realized, injecting known gas quantities and estimating them using the proposed mathematical model and the Kalman-Bucy (KB) estimation method. The estimates obtained reproduce the known production rates much better than standard methods; in particular, the mean error when fitting the known production rates is 15.6 +/- 0.9 vs. 186 +/- 36 ml/min obtained using a conventional method. Experiments with 11 humans were carried out as well, where Vo(2) and Vco(2) were estimated. The variance of the estimation errors, produced by the KB method, appears relatively small and rapidly convergent. Spectral analysis is performed to assess the residual noise content in the estimates, revealing large improvement: 2.9 +/- 0.8 vs. 3,440 +/- 824 (ml/min)(2) and 1.8 +/- 0.5 vs. 2,057 +/- 532 (ml/min)(2), respectively, for Vo(2) and Vco(2) estimates. Consequently, the accuracy of the computed RQ is also highly improved (0.3 x 10(-4) vs. 800 x 10(-4)). The presented study demonstrates the validity of the proposed model and the improvement in the results when using a KB estimation method to resolve it.

Carbon Dioxide↗
PubMed1999

A mathematical model of in situ freezing in liquid nitrogen.

In situ freezing is a procedure, typically applied in neuroscience, to halt metabolism and diffusion. However, the freezing process is not instantaneous, and the regional concentrations of a compound under study may change before the tissue is completely frozen. Knowing the local freezing time, metabolic rate and the diffusion coefficient of the compound of interest, it should be possible to reconstruct the spatial concentration profile prevailing before the object was placed in the cryogen. A mathematical model for calculating the temperature changes at different depths in rabbit and rat heads cooled in liquid nitrogen has been developed. By comparing with experimental results it has been found that the mathematical model can be used for prediction of the local freezing time with a small error.

Animals↗
PubMed2005

Mathematical model to characterize internal filtration.

Convective-diffusive dialysis techniques have recently gained considerable favor. Indeed, convective fluxes through dialyzer membranes have been demonstrated to play a role in enhancing the clearance of middle-molecular-weight solutes. An interesting opportunity is given by exploiting the internal filtration (IF)/back filtration mechanism that occurs spontaneously in high-flux dialyzers, but is difficult to quantify. In view of overcoming this drawback, a semi-empirical, lumped-parameter mathematical model for characterization of IF phenomena was developed. The model considers a dialyzer as composed by N adjacent axial blocks. For each block, hydrodynamics in the blood and dialysate compartments are determined considering hydraulic resistance and calculating local filtration. Blood viscosity and oncotic pressure are calculated locally based on hematocrit and protein concentration. Resistance parameters were determined experimentally for the BS-UL (Toray Industries Inc., Tokyo, Japan) dialyzers. The set of equations describing the model, implemented into a software program, is solved using a numerical method. Simulations allow highlighting the role of device-, treatment- and patient-dependent parameters in affecting IF. Provided an extensive validation is carried out, the use of a mathematical model could be the key to make IF more understandable and its use reliable in clinical practice.

Computer Simulation↗
PubMed2006

A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment.

Glioblastoma, the most malignant form of brain cancer, is responsible for 23% of primary brain tumors and has extremely poor outcome. Confounding the clinical management of glioblastomas is the extreme local invasiveness of these cancer cells. The mechanisms that govern invasion are poorly understood. To gain insight into glioblastoma invasion, we conducted experiments on the patterns of growth and dispersion of U87 glioblastoma tumor spheroids in a three-dimensional collagen gel. We studied two different cell lines, one with a mutation to the EGFR (U87DeltaEGFR) that is associated with increased malignancy, and one with an endogenous (wild-type) receptor (U87WT). We developed a continuum mathematical model of the dispersion behaviors with the aim of identifying and characterizing discrete cellular mechanisms underlying invasive cell motility. The mathematical model quantitatively reproduces the experimental data, and indicates that the U87WT invasive cells have a stronger directional motility bias away from the spheroid center as well as a faster rate of cell shedding compared to the U87DeltaEGFR cells. The model suggests that differences in tumor cell dispersion may be due to differences in the chemical factors produced by cells, differences in how the two cell lines remodel the gel, or different cell-cell adhesion characteristics.

Brain Neoplasms↗
PubMed2006

An integrated agent-mathematical model of the effect of intercellular signalling via the epidermal growth factor receptor on cell proliferation.

We have previously developed Epitheliome, a software agent representation of the growth and repair characteristics of epithelial cell populations, where cell behaviour is governed by a number of simple rules. In this paper, we describe how this model has been extended to incorporate an example of a molecular 'mechanism' behind a rule-in this case, how signalling by both endogenous and exogenous ligands of the epidermal growth factor receptor (EGFR) can impact on the proliferation of cell agents. We have developed a mathematical model representing release of endogenous ligand by cells, three-dimensional diffusion of the secreted molecules through a volume of cell culture medium, ligand-receptor binding, and bound receptor internalization and trafficking. Information relating to quantities of molecular species associated with each cell agent is frequently exchanged between the agent and signalling models, and the ratio of bound to free receptors determines cell cycle progression and hence the proliferative behaviour of the cell agents. We have applied this integrated model to examine the effect of plating density on tissue growth via autocrine/paracrine signalling. This predicts that cell growth is dependent on the concentration of exogenous ligand, but where this is limited, then growth becomes dependent on cell density and the availability of endogenous ligand. We have further modified the calcium concentration of the medium to modulate the formation of intercellular bonds between cells and shown that the increased propensity for cells to form colonies in physiological calcium does not result in significantly different patterns of receptor occupancy. In conclusion, our approach demonstrates that by combining agent-based and mathematical modelling paradigms, it is possible to probe the complex feedback relationship between the behaviour of individual cells and their interaction with one another and their environment.

Animals↗
PubMed1994

Segregated mathematical model for the fed-batch cultivation of a high-producing strain of Penicillium chrysogenum.

A new segregated mathematical model for the penicillin fed-batch process is presented and applied to the growth of the pellet-forming, industrially used high-producing strain Penicillium chrysogenum S2. The model comprises two kinds of biomass (growing and producing, nongrowing and still producing), cell lysis, and complex medium as an important substrate for primary growth. In accordance with our experimental observation, product formation is not inhibited by glucose, but related to the growth rate. Maintenance metabolism is cell age-dependent. The model was verified with two sets of experimental data including exhaust gas measurements while keeping the estimated parameters almost constant. The presented model derived from that of Bajpai and Reuss (1980, 1981) does not describe our data properly. The particular influence of the pellet structure on the model is discussed. The necessity of new model assumptions (e.g., different kinds of biomass, non-constant maintenance coefficient) is explained by cell damage by lysis and shear forces, and the succeeding repair processes.

Biotechnology↗
PubMed1987

A mathematical model for insulin kinetics and its application to protein-deficient (malnutrition-related) diabetes mellitus (PDDM).

A nonlinear mathematical model which incorporates both beta-cell kinetics and a glucose-insulin feedback system is proposed for describing the time variations of plasma glucose and insulin levels. Numerical simulations show that this model is consistent with experimental observations on normal groups. An analysis of the changes in the solutions with variations in the parameters showed that a decrease in a single parameter gave results consistent with experimental findings in protein-deficient (malnutrition-related) diabetes mellitus (PDDM). The model predicts that it is the function and not the number of beta cells which is reduced in PDDM.

Blood Glucose↗
PubMed1991

Application of mathematical model to multiple-dose experimental chemotherapy for fatal murine pneumonia.

Two beta-lactam antibiotics, cefazolin and cefmenoxime, were administered for 7 days to mice with pneumonia caused by Klebsiella pneumoniae by using dosage regimens that would simulate multiple dosing in usual clinical treatments at dosing intervals of 8 or 12 h. Viable numbers of the bacteria in the lungs were measured at 12- or 24-h intervals. The mathematical model established in a previous single-dose study was applied in this study to explain the time courses of the changes in bacterial count over 7 days. However, because the error in viable count measurements was larger than that in the previous study, the time course of the changes in mean viable count was not regular and the viable count reduction rate changed during multiple dosing, and therefore it was difficult to explain the time course by repeated application of the mathematical model described previously. This study suggests that the changes in pharmacokinetic and pharmacodynamic parameters during multiple dosing need to be considered.

Animals↗
PubMed1995

A mathematical model for predicting the temperature distribution in laser-induced hyperthermia. Experimental evaluation and applications.

A time-dependent mathematical model for the heat transfer in laser-induced hyperthermia has been developed. The model calculates the temperature distribution in surface-irradiated tissues. Good agreement was found between the predictions of the model and in vitro experimental results obtained for bovine liver irradiated with an expanded beam from a Nd:YAG laser. Surface evaporation of water was included in the model and experimentally verified. The discrepancy between the measured and the calculated rise in temperature at three different depths on the axis of symmetry of the irradiating beam was found to be less than 5% after 15 min of irradiation. When irradiating in air and not accounting for the surface evaporation in the model, the accuracy of the model predictions was only 75-80%. The model was then used to investigate the influence of surface evaporation of water on the total temperature distribution theoretically in a clinically relevant case. From the numerical simulations, it was shown that, simply by providing a moistened liver surface, the maximum steady-state temperature could be forced into the tissue to a depth of 4 mm. It was also shown that, by employing the numerical model during the initial phase of hyperthermia treatment, overshooting of the temperature during the transient thermal build-up time could be prevented.

Animals↗
PubMed2000

A mathematical model of uterine dynamics and its application to human parturition.

We have developed a simple mathematical model with three physiologically significant states to describe the changes in intrauterine pressure associated with a contraction during human parturition. The myometrium is modelled as a set of smooth muscle cells, each of which is in one of three states (quiescent, contracted, refractory) at a given time. These states are occupied according to a cycle governed by three temporal parameters. The solutions of the equations describing the model show an oscillatory behavior for particular values of these parameters, which is very similar to the time dependent development of intrauterine pressure during labor. Due to its non-linear terms, our model could lead to chaotic oscillations (in the mathematical sense), whose clinical counterpart may occur in cases of dystocia. Despite its simplicity, this model appears to be a useful guide to further investigations of the oscillatory behavior of the myometrium, or other smooth muscles, in normal and pathological situations.

Dystocia↗
PubMedDate not supplied

The use of the PD Adequest mathematical model in pediatric patients on chronic peritoneal dialysis.

OBJECTIVE: To test the accuracy of the PD ADEQUEST kinetic model in calculating peritoneal transport parameters and to quantify the differences between the results of software simulations and direct measurements in order to assess the reliability of this tool in chronic peritoneal dialysis (PD) pediatric patients. PATIENTS: Twenty-nine patients (mean age: 10 +/- 4 years; range: 4-17), 5 on continuous ambulatory PD, 4 on continuous cycling PD, 19 on nocturnal intermittent PD and 1 in nocturnal tidal PD, all free from peritonitis in the previous 2 months. Fourteen patients were anuric and 15 had a mean glomerular filtration rate of 1.79 +/- 1.23 mL/min, range 0.25-4.82. METHODS: In all patients, 24-hour dialysate and urine collections associated to standard peritoneal equilibration test (PET) were performed using their usual dialytic regimen and fill volume (1023 +/- 159 mL/m2 BSA, range 614-1361). PD ADEQUEST kinetic parameters were compared with pediatric and adult data from literature. The measured weekly normalized total creatinine clearance (CRCL), weekly total Kt/V, and daily net ultrafiltration (UF) were compared with corresponding mathematically modeled values. RESULTS: Kinetic parameters calculated by the PD ADEQUEST program were comparable to adult and pediatric values from previous studies after normalization for BSA. Measured and modeled CRCL and Kt/V showed a good agreement [concordance correlation (rc) 0.937 and 0.768, respectively] with limited median percentage absolute errors (11.6% and 10.2%, respectively). Ultrafiltration showed less favorable results (rc = 0.600 and median percentage absolute error 45%) probably owing to the wide variability of this parameter. When the analysis was restricted to the peritoneal component, the rc coefficients results were 0.745 for CRCL and 0.512 for Kt/V (median absolute error: 11.6% and 15.2%, respectively). CONCLUSIONS: The overall findings of our study show that the PD ADEQUEST kinetic model can be used in pediatric patients for the calculation of kinetic indexes and for mathematical simulation of the various regimens. We also feel that the results yielded by the PD ADEQUEST program are reliable enough for this computerized mathematical model to be used in the prescription management of pediatric patients. Only UF prediction needs to be used with a certain caution on account of the marked variability of this parameter.

Adult↗
PubMed2005

Mathematical models of periodic breathing and their usefulness in understanding cardiovascular and respiratory disorders.

Periodic breathing is an unusual form of breathing with oscillations in minute ventilations and with repetitive apnoeas or near apnoeas. Reported initially in patients with heart failure or stroke, it was later recognized to occur especially during sleep. The recurrent hypoxia and surges of sympathetic activity that often occur during the apnoeas have serious health consequences. Mathematical models have helped greatly in the understanding of the causes of recurrent apnoeas. It is unlikely that every instance of periodic breathing has the same cause, but many result from instability in the feedback control involved in the chemical regulation of breathing caused by increased controller and plant gains and delays in information transfer. Even when it is not the main cause of the periodic breathing, unstable control modifies the ventilatory pattern and sometimes intensifies the recurrent apnoeas. The characteristics of disturbances to breathing and their interaction with the control system can be critical in determining ventilation responses and the occurrence of periodic breathing. Large abrupt changes in ventilation produced, for example, in the transition from waking to sleep and vice versa, or in the transition from breathing to apnoea, are potent factors causing periodic breathing. Mathematical models show that periodic breathing is a 'systems disorder' produced by the interplay of multiple factors. Multiple factors contribute to the occurrence of periodic breathing in congestive heart failure and cerebrovascular disease, increasing treatment options.

Animals↗
PubMedDate not supplied

[Mathematical modeling of optimal dose fields in radiotherapy of malignant tumors. Part 2 (Contact methods of radiotherapy)].

The principles of mathematical modeling of optimal dose fields in contact radiotherapy (RT) of malignant tumors are investigated. The point dose additivity provides for presetting the permissible dose field in an irradiated organism as a system of linear limitations to doses in the control points (CP) distributed in the lesion focus and in healthy organs and tissues. It was shown as impossible to shape a dose field by linear limitations to doses in CP in using the RT contact methods with the irradiation sources being implanted into lesion focus. A mathematic interpretation was suggested for the task (with its solution by an iterative algorithm) of forming an optimal dose field in the lesion focus with implanted irradiation sources, which is based on maximizing the factor of dose-field homogeneity. It was further demonstrated that linear limitations, if added to the dose in healthy organs and tissues, make the task even more complicated if not insoluble. Finally, it is suggested to use the method of shaping an effective dose field by the iterative method with interactive visual optimization of the dose field.

Algorithms↗
PubMed1989

A mathematical model of the exercise functional state of the oxygen transport system.

Based on the principle of minimum power, a mathematical model of the exercise functional state of the oxygen transport system is presented. Aerobic and anaerobic muscular efficiencies are considered. The energetically optimal arteriovenous oxygen content difference, cardiac output and ventilation during exercise in man are determined depending on mechanical power. Theoretical results are compared with experimental data.

Animals↗
PubMed2006

Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies.

Angiogenesis, the growth of a network of blood vessels, is a crucial component of solid tumour growth, linking the relatively harmless avascular growth phase and the potentially fatal vascular growth phase. As a process, angiogenesis is a well-orchestrated sequence of events involving endothelial cell migration, proliferation; degradation of tissue; new capillary vessel (sprout) formation; loop formation (anastomosis) and, crucially, blood flow through the network. Once there is blood flow associated with the nascent network, the subsequent growth of the network evolves both temporally and spatially in response to the combined effects of angiogenic factors, migratory cues via the extracellular matrix and perfusion-related haemodynamic forces in a manner that may be described as both adaptive and dynamic. In this paper we present a mathematical model which simultaneously couples vessel growth with blood flow through the vessels--dynamic adaptive tumour-induced angiogenesis (DATIA). This new mathematical model presents a theoretical and computational investigation of the process and highlights a number of important new targets for therapeutic intervention. In contrast to earlier flow models, where the effects of perfusion (blood flow) were essentially evaluated a posteriori, i.e. after generating a hollow network, blood flow in the model described in this paper has a direct impact during capillary growth, with radial adaptations and network remodelling occurring as immediate consequences of primary anastomoses. Capillary network architectures resulting from the dynamically adaptive model are found to differ radically from those obtained using earlier models. The DATIA model is used to examine the effects of changing various physical and biological model parameters on the developing vascular architecture and the delivery of chemotherapeutic drugs to the tumour. Subsequent simulations of chemotherapeutic treatments under different parameter regimes lead to the identification of a number of new therapeutic targets for tumour management.

Animals↗
PubMedDate not supplied

[Evaluation of the effect of cardiotropic agents using a mathematical model of electromechanical coupling].

An assessment of the ionic action mechanism of cardiotropic substances with the aid of a mathematical model for excitation-contraction coupling in myocardium is proved to be possible. The technique developed consists in the model parameter identification from the experimental data on electrical and mechanical activity of myocardial strip. The validity of the technique is tested using the known mechanism drugs. An example is given of analysis by the technique suggested of the action mechanism of diltiazem on the rat papillary muscle.

Animals↗
PubMed2007

A mathematical model of zinc absorption in humans as a function of dietary zinc and phytate.

The quantities of zinc and phytate in the diet are the primary factors determining zinc absorption. A mathematical model of zinc absorption as a function of dietary zinc and phytate can be used to predict dietary zinc requirements and, potentially, enhance our understanding of zinc absorption. Our goal was to develop a model of practical and informative value based on fundamental knowledge of the zinc absorption process and then fit the model to selected published data to assess its validity and estimate parameter values. A model of moderate mathematical complexity relating total zinc absorption to total dietary zinc and total dietary phytate was derived and fit to 21 mean data from whole day absorption studies using nonlinear regression analysis. Model validity, goodness of fit, satisfaction of regression assumptions, and quality of the parameter estimates were evaluated using standard statistical criteria. The fit had an R(2) of 0.82. The residuals were found to exhibit a normal distribution, constant variance, and independence. The parameters of the model, A(MAX), K(R), and K(P), were estimated to have values of 0.13, 0.10, and 1.2 mmol/d, respectively. Several of these estimates had wide CI attributable in part to the small number and the scatter of the data. The model was judged to be valid and of immediate value for studying and predicting absorption. A version of the model incorporating a passive absorption mechanism was not supported by the available data.

Humans↗