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At least 631 records · Page 35Linked to original sources
PubMed1986

A global mathematical model of the cerebral circulation in man.

A mathematical model of the cerebral circulation has been formulated. It was based on non-linear equations of pulsatile fluid flow in distensible conduits and applied to a network simulating the entire cerebral vasculature, from the carotid and vertebral arteries to the sinuses and the jugular veins. The quasilinear hyperbolic system of equations was numerically solved using the two-step Lax-Wendroff scheme. The model's results were in good agreement with pressure and flow data recorded in humans during rest. The model was also applied to the study of autoregulation during arterial hypotension. A close relationship between cerebral blood flow (CBF) and capillary pressure was obtained. At arterial pressure of 80 mmHg, the vasodilation of the pial arteries was unable to maintain CBF at its control value. At the lower limit of autoregulation (60 mm Hg), CBF was maintained with a 25% increase of zero transmural pressure diameter of nearly the whole arterial network.

Blood Pressure↗
PubMed1995

Mathematical modelling of HIV infection therapy.

The previously developed mathematical model simulates the CD4+ lymphocyte dynamics in HIV infection very well. As the number of these cells is a good indicator of the infection progression, it was used to evaluate the effectiveness of different therapeutic interventions. For chemotherapy simulation, both permanent and temporary zinovudine (AZT) administration were considered and the induced return of the CD4+ lymphocyte counts was analysed. Similar analysis was performed for active and passive immunotherapy. The model offers also the possibility of stimulating the CD4+ dynamics after depletion of CD8+ lymphocytes by antibodies. Even one simulated administration of anti-CD8 antibodies increases the CD4+ lymphocyte counts and prolongs the survival of the patient. However, if cells involved in protective immunity are assumed to belong to the CD8+ category, anti-CD8 antibodies accelerate the decrease of CD4- cells and thus shorten the patient's survival.

CD4-Positive T-Lymphocytes↗
PubMed2004

Influence of viscosity on myocardium mechanical activity: a mathematical model.

We have previously proposed and validated a mathematical model of myocardium contraction-relaxation cycle based on current knowledge of regulatory role of Ca2+ and cross-bridge kinetics in cardiac cell. That model did not include viscous elements. Here we propose a modification of the model, in which two viscous elements are added, one in parallel to the contractile element, and one more in parallel to the series elastic element. The modified model allowed us to simulate and explain some subtle experimental data on relaxation velocity in isotonic twitches and on a mismatch between the time course of sarcomere shortening/lengthening and the time course of active force generation in isometric twitches. Model results were compared with experimental data obtained from 28 rat LV papillary muscles contracting and relaxing against various loads. Additional model analysis suggested contribution of viscosity to main inotropic and lusitropic characteristics of myocardium performance.

Animals↗
PubMed2005

A mathematical model for indirectly transmitted diseases.

We consider a mathematical model for the indirect transmission via a contaminated environment of a microparasite between two spatially distributed host populations having non-coincident spatial domains. The parasite is benign in a first population and lethal in the second one. Global existence results are given for the resulting reaction-diffusion system coupled with an ordinary differential equation. Then, invasion and persistence of the parasite are studied. A simplified model for the transmission of a hantavirus from bank vole to human populations is then analysed.

Algorithms↗
PubMed2003

Feedback regulation in the lactose operon: a mathematical modeling study and comparison with experimental data.

A mathematical model for the regulation of induction in the lac operon in Escherichia coli is presented. This model takes into account the dynamics of the permease facilitating the internalization of external lactose; internal lactose; beta-galactosidase, which is involved in the conversion of lactose to allolactose, glucose and galactose; the allolactose interactions with the lac repressor; and mRNA. The final model consists of five nonlinear differential delay equations with delays due to the transcription and translation process. We have paid particular attention to the estimation of the parameters in the model. We have tested our model against two sets of beta-galactosidase activity versus time data, as well as a set of data on beta-galactosidase activity during periodic phosphate feeding. In all three cases we find excellent agreement between the data and the model predictions. Analytical and numerical studies also indicate that for physiologically realistic values of the external lactose and the bacterial growth rate, a regime exists where there may be bistable steady-state behavior, and that this corresponds to a cusp bifurcation in the model dynamics.

Computer Simulation↗
PubMed2003

A mathematical model for elongation of a peptide chain.

A mathematical model is presented for the steps in the elongation process, and the steady-state elongation rate as a function of the amino acid concentrations is found. In addition, the reset sub-process of the elongation process is modeled. The rate of elongation of peptide chains is found to be a function of the concentration of the amino acid to be bound and the concentration of all other amino acids. In addition, the overall elongation rate depends on the concentrations of elongation factors.

Amino Acids↗
PubMed2001

A mathematical model describing the thermal virus inactivation.

A new mathematical model is proposed to describe the inactivation of viruses at different temperatures. This model takes into account the exponential decrease of the viral titer with time, the inactivation rate being an exponential function of the temperature. A one-step non-linear regression was used to fit oral poliovirus vaccine (OPV) experimental data. In one of the applications of the model, we illustrate the use of our model to compare the accelerated degradation test of OPV new formulations to standard OPV. Such a model is both simple and convenient to use. It should be a useful tool in optimizing formulations for live viral vaccines.

Drug Stability↗
PubMed1998

A mathematical model of HIV transmission in NSW prisons.

A mathematical model was developed to estimate HIV incidence in NSW prisons. Data included: duration of imprisonment; number of inmates using each needle; lower and higher number of shared injections per IDU per week; proportion of IDUs using bleach; efficacy of bleach; HIV prevalence and probability of infection. HIV prevalence in IDUs in prison was estimated to have risen from 0.8 to 6.7% (12.2%) over 180 weeks when using lower (and higher) values for frequency of shared injections. The estimated minimum (and maximum) number of IDU inmates, infected with HIV in NSW prisons was 38 (and 152) in 1993 according to the model. These figures require confirmation by seroincidence studies.

Databases, Factual↗
PubMed1991

A mathematical model of rinderpest infection in cattle populations.

A mathematical model for the epidemiology of rinderpest was developed, starting from a simplified descriptive analysis of the disease. A formula for the calculation of the probability of infection of a susceptible animal was first established. A deterministic failure threshold of the infection was then deduced. Deterministic and stochastic approaches were adopted using iterative methods on a computer. These allowed a description of the spread and the variability of an infection process in a population to be made. An illustration of the use of this model showed that, in some cases, variability effects due to stochastic factors were very important. In these particular conditions, the use of the deterministic model alone was not adequate for a good description of the infection. Consequently, improvements of the model were proposed in order to make it more realistic and to allow its use for the evaluation of the efficiency of field operations.

Animals↗
PubMed1999

Simulation of pathological ocular counter-roll and skew-torsion by a 3-D mathematical model.

A basic version of a 3-D mathematical model for simulation of otolithic control of binocular static eye position was extended by introducting excitatory commissural fibers between the vestibular nuclei, and physiological non-linearities: the force-response relationship of utricular neurons and a quadratic relationship between eye muscle innervation and force. These modifications appeared to be necessary in order to simulate the gain asymmetry of ocular counter-roll to lateral head tilt in patients with unilateral utricular loss. The current model can adequately simulate skew-torsion in patients with unilateral utricular loss, lesions of the vestibular nuclei, and central graviceptive pathway lesions. The direction of simulated skew-torsion corresponds satisfactorily to data from normals and patients with acute vestibular loss. The relatively low values of predicted eye deviations for peripheral vestibular lesions suggest that part of the effects seen in patients is caused by affection of the semicircular canals.

Action Potentials↗
PubMed2005

Mathematical modeling of tumorigenesis: mission possible.

PURPOSE OF REVIEW: Mathematical modeling of tumorigenesis is a fast-growing area of research. This review describes recent (since July 2003) advances in this area and discusses possible implications for the field of cancer biology in general. RECENT FINDINGS: Broadly speaking, there are three major areas in which theory has contributed the most to cancer research: (1) modeling in the context of epidemiology and other statistical data, (2) mechanistic modeling of avascular and vascular tumor growth, and (3) modeling of cancer initiation and progression as somatic evolution. The first area uses models to fit the existing data, the second approach takes advantage of methods of physics and engineering to describe tumor growth, and the third method looks at cancer progression as a local, Darwinian evolution. SUMMARY: The article describes new, interesting ideas put forward in the last year, and suggests that to make the modeling effort more relevant, a better dialogue should be developed between theorists and experimental biologists. The author believes this is possible.

Aging↗
PubMed1976

An improved mathematical model of human thyroid hormone regulation.

1. A mathematical model has been constructed of human thyroid hormone regulation by the anterior pituitary gland, which takes account of most of the currently available experimental data. 2. Successful simulation of data on the stimulation of thyrotrophin (TSH) secretion by thyrotrophin releasing hormone (TRH) was achieved assuming that the TSH secretion rate is proportional to the logarithm of the concurrent blood TRH level. 3. Data on the regulation of triiodothyronine (T3) secretion by TSH and the inhibition of TSH secretion by thyroid hormones in contrast could not be simulated on the assumption of instantaneous proportional responses. A mixture of proportional and integral control--the latter taking account of the past history of plasma levels of the regulatory hormone--appeared to be operating at both levels. 4. The pituitary gland appears to be more sensitive to a given fractional change in TRH secretion rate than to the same fractional change in T3 plasma concentration.

Humans↗
PubMed1998

Mathematical modelling of drug transport in emulsion systems.

Two mathematical models for the prediction of drug transport in triphasic (oil, water and micellar) emulsion systems as a function of micellar concentration have been developed and these models were evaluated by comparing experimental and simulated data. Fick's first law was used to derive a transport model for hydrophilic drugs, assuming that the oil/water (o/w) partitioning process was fast compared with membrane transport and therefore drug transport was limited by the membrane. Consecutive rate equations were used to model transport of hydrophobic drugs in emulsion systems assuming that the o/w interface acts as a barrier to drug transport. Benzoic acid and phenol were selected as hydrophilic model drugs. Phenylazoaniline and benzocaine were selected as hydrophobic model drugs. Transport studies at pH 3.0 and 7.0 were conducted using side-by-side diffusion cells. According to the hydrophilic model, an increase in micellar concentration is expected to decrease drug transport rates. The effective permeability coefficients (Peff) of drugs were calculated using an equation relating Peff and the total apparent volume of drug distribution (determined experimentally using drug/membrane permeability and partition coefficient values). The hydrophobic model was fitted to the experimental data for the cumulative amount of model drug in the receiver cells using a weighted least-squares estimation program (PCNONLIN). The oil/continuous phase partitioning rates (k1) and the membrane transport rates (k2) were estimated. The goodness of fit was assessed from the correlation coefficients of plots of predicted versus experimental data. The predicted data were consistent with the experimental data for both the hydrophilic and hydrophobic models.

Aniline Compounds↗
PubMed1992

A lumped parameter mathematical model of the splanchnic circulation.

A lumped parameter mathematical model to describe the propulsion of blood in the splanchnic circulation was developed by integrating the principles of mechanics and physiology. A set of governing equations by derived by specifically considering the contractility of the portal vein, hepatic vein, liver sinusoids, and of the draining lymphatics. These equations were then simulated on a computer. The present simulation results substantiate previous experimental observations that hepatic venous pressure leads to portal hypertension and increased liver interstitial fluid volume.

Blood Pressure↗
PubMed1994

A mathematical model of a rabbit sinoatrial node cell.

A mathematical model for the electrophysiological responses of a rabbit sinoatrial node cell that is based on whole cell recordings from enzymatically isolated single pacemaker cells at 37 degrees C has been developed. The ion channels, Na(+)-K+ and Ca2+ pumps, and Na(+)-Ca2+ exchanger in the surface membrane (sarcolemma) are described using equations for these known currents in mammalian pacemaker cells. The extracellular environment is treated as a diffusion-limited space, and the myoplasm contains Ca(2+)-binding proteins (calmodulin and troponin). Original features of this model include 1) new equations for the hyperpolarization-activated inward current, 2) assessment of the role of the transient-type Ca2+ current during pacemaker depolarization, 3) inclusion of an Na+ current based on recent experimental data, and 4) demonstration of the possible influence of pump and exchanger currents and background currents on the pacemaker rate. This model provides acceptable fits to voltage-clamp and action potential data and can be used to seek biophysically based explanations of the electrophysiological activity in the rabbit sinoatrial node cell.

Animals↗
PubMed2000

Mathematical model of an avian urine concentrating mechanism.

A mathematical model was used to investigate how concentrated urine is produced within the medullary cones of the quail kidney. Model simulations were consistent with a concentrating mechanism based on single-solute countercurrent multiplication and on NaCl cycling from ascending to descending limbs of loops of Henle. The model predicted a urine-to-plasma (U/P) osmolality ratio of approximately 2.26, a value consistent with maximum avian U/P osmolality ratios. Active NaCl transport from descending limb prebend thick segments contributed 70% of concentrating capability. NaCl entry and water extraction provided 80 and 20%, respectively, of the concentrating effect in descending limb flow. Parameter studies indicated that urine osmolality is sensitive to the rate of fluid entry into descending limbs and collecting ducts at the cone base. Parameter studies also indicated that the energetic cost of concentrating urine is sensitive to loop of Henle population as a function of medullary depth: as the fraction of loops reaching the cone tip increased above anatomic values, urine osmolality increased only marginally, and, ultimately, urine osmolality decreased.

Algorithms↗
PubMed2001

Best compliance during a decremental, but not incremental, positive end-expiratory pressure trial is related to open-lung positive end-expiratory pressure: a mathematical model of acute respiratory distress syndrome lungs.

A mathematical model of the acute respiratory distress syndrome (ARDS) lung, incorporating simulated gravitational superimposed pressure and alveolar opening and closing pressures, was used to study the mean tidal pressure-volume (PV) slope ("effective compliance") during incremental and decremental positive end-expiratory pressure (PEEP) trials with constant tidal volume (VT) "ventilation." During incremental PEEP, the PEEP giving maximum mean tidal PV slope did not coincide with "open lung PEEP" (minimum PEEP preventing end expiratory collapse of 97.5% of alveoli inflated at end-inspiration), and it varied greatly with varying VT and "lung mechanics." Incremental PEEP with a low VT tests recruitment by the peak pressure, not prevention of collapse by PEEP. During decremental PEEP with a low VT, maximum mean tidal PV slope occurred with PEEP 2-3.5 cm H2O below open-lung PEEP, unless closing pressure was high. High VT, high "specific compliance," and high opening pressures caused slightly greater underestimation of open-lung PEEP. Maximum mean tidal PV slope was always higher (e.g., 93.7 versus 16.69 ml/cm H2O), and the variation in PV slope with PEEP was greater, during decremental PEEP. The maximum PV slope during a decremental PEEP trial with a low VT may be a useful method to determine open-lung PEEP in ARDS, and should be studied clinically.

Lung Compliance↗
PubMed1999

Mathematical modelling of avascular-tumour growth. II: Modelling growth saturation.

We build on our earlier mathematical model (Ward & King, 1997, IMA J. Appl. Math Appl. Med. Biol., 14, 39-69) by incorporating two necrotic depletion mechanisms, which results in a model that can predict all the main phases of avascular-tumour growth and heterogeneity. The model assumes a continuum of live cells which, depending on the concentration of a generic nutrient, may reproduce or die, generating local volume changes and thus producing movement described by a velocity field. The necrotic material is viewed as basic cellular material (i.e. as a generic mix of proteins, DNA, etc.) which is able to diffuse and is utilized by living cells as raw material to construct new cells during mitosis. Numerical solution of the resulting system of partial differential equations shows that growth ultimately tends either to a steady-state (growth saturation) or becomes linear. Both the travelling-wave and steady-state limits of the model are therefore derived and studied. The analysis demonstrates that, except in a very special case, passage of cellular material across the tumour surface is necessary for growth saturation to occur. Using numerical techniques, the domains of existence of the large-time solutions are explored in parameter space. For a particular limit, asymptotic analysis makes explicit the main phases of growth and gives the location of the bifurcation between the long-time outcomes.

Models, Biological↗