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At least 775 records · Page 43Linked to original sources
PubMedDate not supplied

A mathematical model of the hsp70 regulation in the cell.

A mathematical model of the regulation process of the heat shock protein hsp70 in the cell is presented. The model describes the damaging effect of elevated temperature on proteins; the interaction of free hsp70 with injured proteins and its chaperone role in nascent protein translation; the relation between the amount of free hsp70 and the formation of the activated trimer form of the heat shock factor protein (HSF); the binding of activated HSF with the heat shock elements on the DNA; the transcription of mRNA of hsp70 and the synthesis of hsp70. The reaction of the model to a temporal rise in temperature shows an initial decline and a subsequent sharp rise to an ultimately increased level of free hsp70 in the cell. The response of the model to both a single and two consecutive heat shocks appears to closely resemble experimental data on hsp70 synthesis. This general agreement demonstrates the structure of the model to be sound and suitable as a basis for further modelling the complex tolerance mechanism of the cell.

Cell Survival↗
PubMedDate not supplied

[Prognostic radioecological mathematical model of the Yenisei river].

A one-dimensional mathematical model of the Yenisei river ecosystem including hydrological, ecosystem and radioecological blocks has been developed. The model was used to evaluate contribution of different processes (transfer by water masses, dilution, radioactive decay, bioaccumulation) into self-purification of the river water from a radiation pollution and calculate pollution density of ecosystem components (bacteria, phyto-, zooplankton, phyto-, zoobenthos, detritus) with 137Cs and 32P.

Ecosystem↗
PubMed1975

Mathematical modelling of cell cycle and chronobiology: preliminary results.

A mathematical model taking into account the observed diurnal variations in cell kinetics is presented. The principle of the method is to divide each phase of the cell cycle in a definite number of compartments and to assume that the fluxes into and out of the compartments corresponding to the G1 phase are the only varying parameters through the day. Theoretical evolutions of percentages of cells in M and S phase, theoretical curves for percentage labelled mitosis experiment are derived. Preliminary results of the applications of the model to interpretation of published experimental data obtained in hamster cheek pouch epithelium are shown.

Cell Division↗
PubMed2002

A mathematical model for the flotation of waste activated sludge.

A mathematical model that describes a batch flotation process is presented. The model employed a similar method to the hindered settling of flocculated material. This idea is based on our experimental results that the time growth curves of separated liquor zone showed a similar character to the settling curve of flocculated material, when the vertical axis reversed. In this model, it is also assumed that the gas phase and solid phase have the same movement, that is microbubbles and solid sludge particles joined to form aggregated floc. By comparing the numerical prediction with experimental data, the usefulness of the model is confirmed and some examples of flotation simulation are demonstrated.

Carbon Dioxide↗
PubMedDate not supplied

Assessment of the age of atherosclerosis risk in population studies using a two factorial mathematical model.

The risk of atherosclerosis was assessed using a mathematical model of competition between LDL and HDL on 365 randomly selected persons. The results speak for the fact that the risk falls between the ages of 30 and 40 years for males, and 40 and 50 years for females. We are of the opinion that our procedure may be valid for sex comparison studies attempting to objectify the prevalence of atherosclerosis in population studies.

Adult↗
PubMed1989

A mathematical model of extracorporeal antibody removal in autoimmune disease.

A mathematical model of T-B cell cooperation is adopted to describe autotolerance and autoimmunity. The model describes the development of plasma cells and T-helper cells from their precursors through activated and proliferating cells. A state of autotolerance is simulated by reducing the rate of T precursors supply (partial clonal deletion theory), while the normal rate yields a stable state of autoimmunity. During the state of autoimmunity extra-corporeal removal of autoantibody and immunosuppression are simulated. Removal of auto-antibody alone results in stimulation of the immune system and quick return to the previous state, mainly on account of activation of memory cells. Antibody overshooting is negligible. Immunosuppression leads to a slow decline in the antibody level. Synergy is clearly demonstrated between both therapies.

Autoantibodies↗
PubMed1982

Which mathematical model to study uremic toxicity? National Cooperative Dialysis Study.

Mathematical modelling advantages and limitations to study dialysis adequacy are evaluated, the use of the single pool urea model in the guidance of the National Cooperative Dialysis Study (NCDS) is described, and therapeutic control results from the Control phase of the NCDS are reported. The relevance of using urea as a target compound and the practicality of modelling its levels in clinical settings using a single pool model are discussed. The NCDS involves intensive participation of 8 geographically separate centers to control BUN at two weekly time averaged concentrations (50 +/- 5 and 100 +/- 5 mg/dl) using standard clinical dialyzers and two different lengths of dialysis (3 and 4.5 hr) in the presence of .8-1.4 g/kg/day protein intake. Control phase data on 195 patients indicates a remarkable level of clinical precision and method reproducibility as well as a high degree of patient compliance. Patient urea volumes averaged 39.8 +/- 8.9 liters, net rates of daily protein catabolism were 1.06 +/- .17 g/kg; daily weight gain: .96 +/0 .43 kg; and dialyzer clearances to maintain patients in the control phase for 3 to 6 months were 168 +/- 44 ml/min. Clearances required to randomize patients into four experimental groups ranged 40-250 ml/min. Less than 1/4 of dialyzers were larger than 1.8 m2 and were not specific to any experimental group.

Blood Urea Nitrogen↗
PubMedDate not supplied

[A simulated mathematical model of the blood coagulation system intrinsic pathway].

A mathematical model of the blood coagulation system intrinsic pathway is developed based on a reaction cascade scheme with two positive feedbacks. The model describes quantitatively well-known experimental data on blood plasma coagulation kinetics for various levels of activation and varying calcium concentrations. In the limit of experimental variety of the values of the rate for individual stages of coagulation cascade, obtained in [5-12], a good agreement with experimental data was shown for two discrete sets of the constants. The model relates unambiguously the threshold properties in coagulation activation by calcium with existence of the activation threshold. The model allows numerical estimates of the threshold activation values for various calcium concentrations. At calcium concentration of 0.2 mM, corresponding to normal calcium content in blood, the activation threshold is equal to 0.00016 nM and 0.0019 nM of Factor XIa for the first and the second sets of the system parameters, respectively.

Blood Coagulation↗
PubMed1980

Aerosol deposition in the respiratory tract of the rat. Experimental results and mathematical modelling.

The deposition fraction in the respiratory tract of rats were determined experimentally using aerosol 85Srl2 in saline. The dimensions of the particles [MMD 1.63 /+- /+- 0.47 micron, Sg = 1.29] were measured by two independent methods. Rats weighing 200 g were exposed for a period of 60 min [t] in the inhalation apparatus PIANO 3 with a generator according to Lauterbach. From the volume activity [A] of 3 - 11 Bq/litre air a depot of 35-129 kBq was formed in the animals. Spirometric values measured with a modified Jäger ergospirometer were: V = 178.8 /+- 42.9 ml, VT = = 1.18 /+- 0.24 ml. f = 163.1 /+- 28.1 cycles/min. The total amount inhaled [Q] was calculated [Q = V.A.t], the deposited amount [D] was measured by a whole body counter. THe mean deposition fraction was 0.570 /+- 0.052 and was not related either to exposure time or to aerosol activity. In view of the broad validity of the conclusions for aerosols of round-shaped particles, the mean deposition fraction was determined with the help of a mathematical model according to Landahl. The theoretical values amounted to 0.609 [from 0.522 to 0.686]. The good agreement between the mean deposition fractions estimated by two independent methods indicates that on the basis of the probability theory and dimensional analysis, the mathematical model can also be used in humans for simulation deposition as one of the basis foundations for a quantitative evaluation of inhalation risk from any kind of aerosol.

Aerosols↗
PubMed1983

A mathematical model of biodegradability screening tests as an aid to interpretation of observed results.

A mathematical model, based on a modification of the Michaelis--Menten and Monod equations describing bacterial growth, has been used to predict the course of removal of the organic substrates in the modified OECD and other screening tests. A range of initial concentrations of bacteria in the inoculum has been selected, using published data on the total bacterial count in secondary sewage effluents and activated sludge, to simulate the wide range of volumes of these materials used in practice. The arbitrary definition of ready biodegradability adopted by the OECD, that is, 5 to the equivalent of 70% DOC removal in not more than 10 days in a total incubation period of 28 days, is expressed in terms of inoculum size and kinetic constants. Modifications are proposed to the screening test with the object of making it more useful and realistic in predicting whether or not a chemical will be removed in sewage treatment.

Bacteria↗
PubMed1993

Mathematical modelling and quantification of the autoinhibitory feedback control of noradrenaline release in brain slices.

Concentration-response curves, reflecting alpha 2-autoreceptor-mediated inhibition of [3H]-noradrenaline release by exogenous noradrenaline in rat cerebral cortex and rabbit hippocampus slices, were analysed in order to test the usefulness of a mathematical model describing the relation between the independent variable, exogenous noradrenaline, and the dependent variable, inhibition of release. This model was based on the assumption of direct proportionality between receptor occupation and response, implying that there is correspondence between the shape of a concentration-binding curve and a concentration-response curve. The experimental concentration-response curves were obtained by different approaches: noradrenaline release from brain slices prelabelled with [3H]-noradrenaline was elicited electrically either by pseudo-one-pulse (POP) stimulation or by stimulation with 36 pulses applied with a frequency of 3 Hz. POP stimulation avoids autoinhibition by released noradrenaline and, therefore, was a suitable touchstone for the applied mathematical model which evaluates by nonlinear regression analysis two primary parameters: the dissociation constant between noradrenaline and the alpha 2-adrenoceptor and the biophase concentration of noradrenaline which reflects the extent of autoinhibition and should be zero under POP conditions. In rat cerebral cortex tissue, the corresponding biophase concentration of endogenous noradrenaline was indeed estimated to be zero and the dissociation constant was Kd = 10(-7.62 +/- 0.14) mol/l. With 3 Hz stimulation, the biophase concentration was 10(-7.80 +/- 0.05) mol/l, which has to be interpreted with respect to a simultaneously estimated Kd of 10(-7.63 +/- 0.12) mol/l.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗
PubMed2004

A history of the study of solid tumour growth: the contribution of mathematical modelling.

A miscellany of new strategies, experimental techniques and theoretical approaches are emerging in the ongoing battle against cancer. Nevertheless, as new, ground-breaking discoveries relating to many and diverse areas of cancer research are made, scientists often have recourse to mathematical modelling in order to elucidate and interpret these experimental findings. Indeed, experimentalists and clinicians alike are becoming increasingly aware of the possibilities afforded by mathematical modelling, recognising that current medical techniques and experimental approaches are often unable to distinguish between various possible mechanisms underlying important aspects of tumour development. This short treatise presents a concise history of the study of solid tumour growth, illustrating the development of mathematical approaches from the early decades of the twentieth century to the present time. Most importantly these mathematical investigations are interwoven with the associated experimental work, showing the crucial relationship between experimental and theoretical approaches, which together have moulded our understanding of tumour growth and contributed to current anti-cancer treatments. Thus, a selection of mathematical publications, including the influential theoretical studies by Burton, Greenspan, Liotta et al., McElwain and co-workers, Adam and Maggelakis, and Byrne and co-workers are juxtaposed with the seminal experimental findings of Gray et al. on oxygenation and radio-sensitivity, Folkman on angiogenesis, Dorie et al. on cell migration and a wide variety of other crucial discoveries. In this way the development of this field of research through the interactions of these different approaches is illuminated, demonstrating the origins of our current understanding of the disease.

Cell Growth Processes↗
PubMed1993

Use of mathematical models for understanding the dynamics of gene amplification.

Recently it has been suggested that high levels of cancer drug resistance and poor prognosis are strongly associated with gene or oncogene amplification (GA). It has been further suggested that the molecular mechanisms underlying GA may be different for different genes, and that different amplification mechanisms may function concurrently or sequentially in the same gene. The aim of this review is to demonstrate the use of mathematical models in studying these intricate dynamics. We have provided mathematical models for the generation of extrachromosomal elements, their autonomous replication and equal or unequal mitotic segregation, the integration of the extrachromosomal elements within the chromosomes, and chromosomal GA in one or many unlinked genes. Using this formal description one can examine the potential role of each GA mechanism in the generation of specific distributions of gene-copy number in a cell population, under various levels of selection stringency. Thus one can specify the conditions for the emergence of drug-resistant mutants prior to selection, as well as the relationships between the stringency of the selecting environment and the characteristics of the resultant cellular phenotype.

Animals↗
PubMed1993

Mathematical model for the selective deposition of inhaled pharmaceuticals.

To accurately assess the potential therapeutic effects of airborne drugs, the deposition sites of inhaled particles must be known. Herein, an original theory is presented for physiologically based pharmacokinetic modeling and related prophylaxis of airway diseases. The mathematical model describes the behavior and fate of particles in the lungs of adult human subjects under various breathing conditions. Their deposition patterns are calculated via superposition of the separate but not independent processes of inertial impaction, sedimentation, and diffusion. The related computer code is designed to calculate total and compartmental (tracheobronchial and pulmonary) distributions of inhaled aerosols. In this manuscript, the model is first tested via comparisons of predicted deposition patterns with laboratory data from human inhalation exposure experiments and then it is applied to determine which factors most influence the dosimetry of inhaled particles. In this format, deposition patterns are explicitly related to particle characteristics, ventilatory parameters, and intersubject variabilities of lung morphologies. The dosimetric model was developed to improve the efficacy of aerosol therapy via the selective deposition of inhaled pharmaceuticals at prescribed lung locations to elicit optimum effects.

Administration, Inhalation↗
PubMed1995

Normal pressure hydrocephalus: an analysis of aetiology and response to shunting based on mathematical modeling.

The dynamics which maintain the state of enlarged cerebral ventricles and normal intracranial pressures (normal pressure hydrocephalus) are not completely understood, making the response to cerebrospinal fluid diversion difficult to predict. Using our previously described mathematical model of intracranial physiology which allows nonlinear relationships of pressure, volume, and flow in 7 distinct compartments, we desired to determine factors which could be responsible for the development and maintenance of the steady state of normal pressure hydrocephalus. Using typical starting values for CSF volume, pressure, and flow, the model indicates that this condition cannot be sustained, in spite of high CSF outflow resistance, unless capillary flow resistance is elevated. This condition can be the result of arterial hypertension. The additional modeling of a CSF diversion device demonstrates predicted time courses for ventricular size reduction which are consistent with clinical observations. We conclude that certain vascular conditions may allow for the maintenance of an enlarged ventricular size, and that mathematical modeling can assist in identifying factors for clinical study that may maintain normal pressure hydrocephalus even after treatment by CSF diversion.

Cerebral Ventricles↗
PubMed1976

Death rates of bacterial spores: mathematical models.

The concave survivor curves produced as a result of spore heterogeneity were analyzed to determine whether they were caused by inmate characteristics of the spores or by the acquisition of heat resistance during the heating process. Mathematical models developed for the two hypotheses revealed that the concave survivor curve (on semi-log paper) caused by innate heterogeneity is parabolic and that caused by acquired heat resistance is exponential. The mathematical models were applied to several published survivor curves of different organisms, and heat resistance parameters and the cause of curvilinearity were determined. For the cases studied, the cause of curvilinearity appears to be acquisition of heat resistance rather than innate heterogeneity of spore population.

Adaptation, Biological↗
PubMed1992

A mathematical model for the quantification of mitral regurgitation. Experimental validation in the canine model using contrast echocardiography.

BACKGROUND: Because the clearance of contrast from the left atrium (LA) relative to the left ventricle (LV) depends on the degree of mitral regurgitation (MR), we hypothesized that a mathematical model can be developed that would provide a quantitative estimation of MR from the washout of contrast from these chambers. METHODS AND RESULTS: After mathematically developing the model, we performed experiments in two groups of dogs with the use of contrast echocardiography. Group 1 consisted of nine dogs in which different degrees of MR were produced by creating ischemic LV dysfunction. Contrast was injected into the LV, and MR was graded visually on a scale of from 0 to 4+. Videointensity plots generated from the LA and LV were provided to the model. There was excellent correlation between visual assessment of MR and model-derived regurgitant fraction in the 33 stages: y = 0.16x + 0.002 (r = 0.97, p less than 0.001, SEE = 0.06). To obtain a more quantitative validation, we placed electromagnetic flow probes on the aorta and just cephalad to the mitral annulus in six dogs (group 2) during cardiopulmonary bypass. Different degrees of MR were produced by chordal traction and/or myocardial ischemia. Regurgitant fraction was calculated at each stage from the flow probe and videointensity data. There was excellent correlation between flow probe and model-derived regurgitant fraction (y = 0.90x + 0.03; r = 0.96, p less than 0.001, SEE = 0.06), and close interobserver and intraobserver correlations were noted using flow probe and contrast echocardiographic data. CONCLUSIONS: A mathematical model that uses the clearance of contrast from the LA relative to the LV can be used to accurately measure the severity of MR. These findings may have important practical implications for the quantification of MR.

Animals↗
PubMed1991

[A mathematical model of the epidemic process in anthroponotic infection with stable and homogeneous factors].

A very simple mathematical model of the epidemic process of human infection in the presence of stable and homogeneous factors has been created and analyzed. The theoretical possibility of describing the detailed course of the epidemic process by means of this model, permitting the consideration of inner parameters which cannot be determined in any other way, has been shown. The study has revealed that the approximation of the model to the real epidemic process is connected with the introduction of the notion of the heterogeneity of the parasite and host populations into the axiomatics of modeling.

Communicable Diseases↗