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At least 1,765 records · Page 98Linked to original sources
PubMed2005

Electromechanics of paced left ventricle simulated by straightforward mathematical model: comparison with experiments.

Intraventricular synchrony of cardiac activation is important for efficient pump function. Ventricular pacing restores the beating frequency but induces more asynchronous depolarization and more inhomogeneous contraction than in the normal heart. We investigated whether the increased inhomogeneity in the left ventricle can be described by a relatively simple mathematical model of cardiac electromechanics, containing normal mechanical and impulse conduction properties. Simulations of a normal heartbeat and of pacing at the right ventricular apex (RVA) were performed. All properties in the two simulations were equal, except for the depolarization sequence. Simulation results of RVA pacing on local depolarization time and systolic midwall circumferential strain were compared with those measured in dogs, using an epicardial sock electrode and MRI tagging, respectively. We used the same methods for data processing for simulation and experiment. Model and experiment agreed in the following aspects. 1) Ventricular pacing decreased systolic pressure and ejection fraction relative to natural sinus rhythm. 2) Shortening during ejection and stroke work declined in early depolarized regions and increased in late depolarized regions. 3) The relation between epicardial depolarization time and systolic midwall circumferential strain was linear and similar for the simulation (slope = -3.80 +/- 0.28 s(-1), R2 = 0.87) and the experiments [slopes for 3 animals -2.62 +/- 0.43 s(-1) (R2 = 0.59), -2.97 +/- 0.38 s(-1) (R2 = 0.69), and -4.44 +/- 0.51 s(-1) (R2 = 0.76)]. We conclude that our model of electromechanics is suitable to simulate ventricular pacing and that the apparently complex events observed during pacing are caused by well-known basic physiological processes.

Algorithms↗
PubMed2006

A mathematical model for the prediction of solute kinetics, osmolarity and fluid volume changes during hemodiafiltration with on-line regeneration of ultrafiltrate (HFR).

Hemodiafiltration with on-line regeneration of ultrafiltrate (HFR) is a technique indicated for the treatment of dialysis patients affected by inflammatory syndrome and malnutrition. In the present work, a mathematical model, which describes intradialytic fluid and solute kinetics during standard diffusive dialysis, has been adapted to analyze solutes and fluid dynamics during HFR. The model is an improved version of our previous ones, and represents a good compromise between simplicity and reliability. It considers the intradialytic kinetics of sodium, potassium and urea, and two body fluid compartments: intracellular and extracellular. Moreover, the model includes simple equations to predict the intradialytic time pattern of osmolarity. The model has been experimentally validated by using 9 HFR sessions on 9 patients (one per each patient), comparing the time course of plasma solutes and osmolarity measured every 30 minutes during HFR, with those predicted by the model. Predictions are performed a priori, i.e., without any parameter adjustment, but just starting from knowledge of a few quantities (plasma sodium, potassium, urea, osmolarity and body weight) at the beginning of the session. The average deviations between model and real data (sodium: 1.9 mEq/L; potassium: 0.32 mEq/L; urea: 1.04 mmol/L; osmolarity: 5.02 mosm/L) are of the same order as measurement errors and similar to those obtained using our previous models in standard and profiled hemodialysis. Moreover, the prediction on sodium concentration only scarcely worsens (from 1.9 to 2.02 mEq/L) if default values are used for the initial value of other solutes in blood (i.e., if the algorithm uses only initial body weight and initial sodium concentration in plasma). The results confirm the good predictive capacity of the model in HFR, and suggest its possible innovative use to optimize sodium balance in HFR, from knowledge of only the sodium concentration in the ultrafiltrate.

Aged↗
PubMed1975

Effects of antiarrhythmic drugs on cardiac membrane conductances; a study using the Hodgkin and Huxley mathematical model.

A study in voltage clamp conditions of the modifications of the cardiac membrane conductances by quinidine sulfate has been carried out on frog atrial fibers by means of the double sucrose gap technique. The computation of the parameters related to the conductances has been done according to the Hodgkin and Huxley mathematical model proposed in 1952. The computed conductances concern the sodium conductance, the calcium conductance, and the total delayed conductance. A decrease of all of the studied conductances is observed in the presence of quinidine sulfate. This drug also mainly induced a slowing down of several activation, inactivation, and reactivation kinetics. The results obtained allow a more detailed explanation of the mechanism of action of quinidine sulfate in the membrane. Although quinidine is known to possess antiarrhythmic properties, the exact mechanisms of its action are not clear. The present study was therefore undertaken to provide some information on this point.

Animals↗
PubMedDate not supplied

[A mathematical model of the status of mitochondrial DNA for assessing the effectiveness of energy biosynthesis in mammalian cells].

A concept is advanced according to which the processes of ageing, non-specific pathology and malignant transformation are caused by mutations of mitochondrial DNA which controls protein synthesis of the oxidation phosphorylation system. A mathematical model is plotted for describing the efficiency of the system of energy supply of mammalian cells as a function of accumulation of mtDNA mutations. It is shown that at a definite degree of heterogeneity of mitochondria population malignant transformation proceeds. Explanations are presented of the existence of a latent period between the effect of cancerogenic agent and occurrence of tumour, mechanism of the realization of remote effects of chronic action of low intensity agents (these explanations are absent in modern theories of cancerogenesis and quantitative radiobiology).

Animals↗
PubMed1996

Two mathematical models explain the variation in cystometrograms of obstructed urinary bladders.

Overdistension of the urinary bladder, secondary to outlet obstruction, causes cellular changes in the bladder wall, including hypertrophy of the smooth muscle cells, which increase bladder mass. To investigate the effects of increased mass on the cystometrogram (CMG), we have developed two mathematical models. In the first model, we assume that mass is added such that the largest bladder volume at zero transmural pressure, the zero pressure volume (ZPV), is constant, It predicts increased pressures and decreased compliance in the CMG. In the second model, we assume that both mass and ZPV increase proportionally. It predicts unchanged pressures, increased compliance, and increased capacity in the CMG. These results allow use to divide animal experiments in the literature into two groups. Cystometrograms performed on animals that have had outlet obstruction induced by a cuff method, inducing a small increase in mass, belong to the first group: hypertrophy with no change in ZPV. Cystometrograms performed on animals that have had outlet obstruction induced by a ligature method, inducing a large increase in mass, belong to the second group: hypertrophy with increased ZPV. We conclude that increased ZPV results from a more severe obstruction which is indicated by the increased capacity and compliance.

Animals↗
PubMed1983

Mathematical modelling of malignant melanoma trends in Norway, 1953-1978.

Epidemiologic studies have documented a rapid rise in the mortality and incidence of malignant melanoma of the skin in many countries. This paper presents an analysis of malignant melanoma time trends in data from the Norwegian Cancer Registry, 1953-1978, by subsite and sex. The purpose of this study is to quantify previous qualitative analysis of the same data, mainly to distinguish birth cohort effects from time period effects. This analysis shows that time trends in malignant melanoma in Norway can be explained economically by a common age effect and a separate cohort effect for each subsite in both sexes or alternatively, by a common cohort effect but different age effects for each sex and subsite. In neither case is a time period effect required. Mathematical modelling can never fully explain any situation exactly and it is more than likely that the increases observed have been produced by a measure of both extreme descriptions. The different cohort effects and age effects are discussed in terms of their implications for etiology.

Adolescent↗
PubMed2005

Long-term mathematical model involving renal sympathetic nerve activity, arterial pressure, and sodium excretion.

This paper presents a physiological long-term model of the cardiovascular system. It integrates the previous models developed by Guyton, Uttamsingh and Coleman. Additionally it introduces mechanisms of direct effects of the renal sympathetic nerve activity (rsna) on tubular sodium reabsorption and renin secretion in accordance with experimental data from literature. The resulting mathematical model constitutes the first long-term model of the cardiovascular system accounting for the effects of rsna on kidney functions in such detail. The objective of developing such a model is to observe the consequences of long-term rsna increase and impairment of rsna inhibition under volume loading. This model provides an understanding of the rsna-related mechanisms, which cause mean arterial pressure increase in hypertension and total sodium amount increase (sodium retention) in congestive heart failure, nephrotic syndrome and cirrhosis.

Animals↗
PubMed2006

Mathematical modeling shows exenatide improved beta-cell function in patients with type 2 diabetes treated with metformin or metformin and a sulfonylurea.

The incretin mimetic exenatide improved glycemic control and reduced body weight in patients with type 2 diabetes inadequately controlled with metformin+/-a sulfonylurea. We assessed postprandial beta-cell function by mathematical modeling, independent of confounding effects from differing ambient glucose levels among treatments. Subjects were 63% males, 55+/-10 years, BMI 33+/-6 kg/m2, HbA1C 8.1+/-1.1% (+/- SD) randomized to 5 microg exenatide or placebo twice daily for 4 weeks. Subsequently, one arm remained at 5 microg twice daily, one arm escalated to 10 microg twice daily, and one treatment arm remained on placebo for 26 weeks. Subjects continued metformin+/-a sulfonylurea. A subset with meal tests at baseline and week 30 were analyzed (n=73). Outcome measures were the model-based beta-cell function parameters dose-response relating insulin secretion to glucose concentration, rate sensitivity, and potentiation. Exenatide reduced postprandial glucose excursions. Modeling predicted an upward shift of the beta-cell dose-response. Model-predicted insulin secretion rate at a reference glucose concentration increased 72% (10 microg), increased 40% (5 microg), or decreased 21% (placebo) at week 30 [ p=0.015 (10 microg); p=0.045 (5 microg); vs. placebo]. At week 30, the 2-hour post-meal to basal potentiation factor ratio was increased to 1.53+/-0.10 (10 microg; p=0.0142 vs. placebo) or 1.40+/-0.08 (5 microg; p=0.0402 vs. placebo) compared with 1.15+/-0.06 (placebo). Exenatide caused an upward shift of the beta-cell dose-response and enhanced potentiation of insulin secretion. This model suggests exenatide improved beta-cell function in patients with type 2 diabetes treated with metformin+/-a sulfonylurea.

Adult↗
PubMed2006

A mathematical model for the mating-induced prolactin rhythm of female rats.

For the first 10 days of pregnancy and the first 12 days of pseudopregnancy, the secretion of prolactin (PRL) from pituitary lactotrophs is rhythmic, with two surges/day. This rhythm can also be triggered by bolus injection of oxytocin (OT). We describe a mathematical model for the initiation, maintenance, and termination of the OT-induced PRL rhythm. In our model, the mechanism for this circadian rhythm is mutual interaction between lactotrophs and neuroendocrine dopamine (DA) neurons. This rhythm is, under normal lighting conditions, entrained by the suprachiasmatic nucleus (SCN) but persists in the absence of input from the SCN. We postulate that OT injection triggers the rhythm by activating a population of bistable hypothalamic neurons that innervate and inhibit DA neurons. The bistable nature of these neurons allows them to act as a memory device, maintaining the rhythm long after OT has been cleared from the blood. The mechanism for this memory device and the arguments supporting it are detailed with computer simulations. Finally, we consider potential targets for a rhythm-terminating factor and make predictions that may be used to determine which mechanism is operational in terminating the OT- or mating-induced PRL rhythm.

Animals↗
PubMed1990

A mathematical model of radiotherapy department dynamics.

Technical managers are increasingly called upon to plan for the future needs of radiotherapy departments. Such planning involves calculating budgetary and staffing requirements, as well as identifying equipment purchases. To anticipate these needs, a means to assess the department's patient capacity is necessary. This article proposes a mathematical model examining patient flow to assist with the expansion plans of radiotherapy departments.

Efficiency↗
PubMedDate not supplied

[Mathematical model of the bone callus tissue obtained during distraction osteosynthesis].

After some surgical interventions it's need to regenerate a part of bone. The new bone formation in the external fixation apparatus is the result of elongation and maturation of the bone callus, originated in pre-destructive period between bone fragments. The mathematical model of bone callus is proposed. Its main structural elements are osteogeneous and cartilage cells, osteoblasts, matrix, blood vessels. The derived equations take account of matrix production, dependent on the stress in tissue, and transformation of one kind of cells into another in accordance with O2 concentration is more or less than some critical value. The material of the callus is considered as a growing elastic body with growth coefficients, dependent on the structural tensor and Ca concentration. The structural tensor represents the anisotropy of fibrils orientation that take place during deformation. The concentrations of O2 and Ca are connected with the density of blood vessels whose propagation is related to the diffusion of a hypothetical substance. The formulated boundary problem allows to define changes in the growing zone of the callus and to define its size as a function of the rate of elongation.

Bony Callus↗
PubMed1997

Three-dimensional dosimetry for intralesional radionuclide therapy using mathematical modeling and multimodality imaging.

UNLABELLED: A method of dosimetry is described that quantifies the three-dimensional absorbed-dose distribution resulting from an intralesional administration of a radiolabeled monoclonal antibody, allowing for both spatial and temporal heterogeneity of distribution of the radionuclide and without the need for a calibration scan. METHODS: A mathematical model was developed to describe the distribution of activity as a function of time resulting from infusion at a single point within the solid component of a tumor. The parameters required for this model are either known directly or may be obtained from SPECT image data registered to computed tomography. Convolution of this distribution with a point-source dose kernel enabled the three-dimensional absorbed-dose distribution to be obtained. RESULTS: This method was applied to a set of patient data acquired in the course of a clinical study performed at our center, and dose profiles and dose-volume histograms were produced. It was shown that the three-dimensional distribution of dose was significantly nonuniform. CONCLUSION: Initial results suggest that this method offers a means of determining the absorbed dose distribution within a tumor resulting from intralesional infusion. This method extends the Medical Internal Radiation Dose computation, which, in these circumstances, would make erroneous assumptions. Furthermore, it will enable individual patient treatment planning and optimization of the parameters that are within the clinician's control.

Humans↗
PubMed1999

A mathematical model for synergistic eukaryotic gene activation.

The precise biochemical mechanism underlying the synergistic action of gene activators on eukaryotic transcription has eluded a solution, largely because of the technical difficulties inherent in analyzing the mechanics of a 2.5 MDa complex comprising greater than 50 polypeptide components. To complement the biochemical approach we have employed mathematical modeling as a means to understand the mechanism of synergy. Parameters relevant to activated transcription were varied in a simple biochemical system and the data were compared to the transcriptional response predicted by a multi-component statistical model. We found that the model achieved a consistent, semi-quantitative description of the measured transcriptional response, and enabled the characterization and measurement of thermodynamic parameters in the in vitro system. The results provide evidence for the existence of cooperativity in the activation process beyond what would be predicted from one current model suggesting that activators function solely by simple recruitment of the general transcription machinery to the promoter.

Binding Sites↗
PubMedDate not supplied

Unilateral neck exploration for primary hyperparathyroidism: analysis of a controversy using a mathematical model.

Most endocrine surgeons explore both sides of the neck and identify all parathyroid glands when operating on patients with primary hyperparathyroidism. Others, however, advocate the unilateral approach, i.e., if an adenoma and a normal gland are identified, the contralateral side is not explored. We analyzed the strategy of the unilateral approach using a mathematical model to determine the variables that influence the probability of missing a tumor on the unexplored side of the neck. Assuming the frequency of single adenoma is 80%, hyperplasia 14%, double adenomas 4%, triple adenomas 1%, and carcinoma 1%, and the probability of missing a tumor on the explored side is 5%, we found that: 1. Only 41% of the patients treated by the unilateral approach undergo unilateral exploration. This is increased to 62% when a localization study with a sensitivity of 80% is used pre-operatively. 2. The probability of missing a tumor on the unexplored side of the neck parallels the prevalence of multiple adenomas. Half of the patients with triple adenomas and two-thirds of the patients with double adenomas will have a missed tumor when treated by the unilateral approach. 3. Patients who undergo unilateral exploration have an additional 7% to 8% probability of missing a tumor that would have been found if bilateral exploration is performed. This risk is lowered to 2% by a pre-operative localization study that is 80% sensitive. 4. A prospective study will require 684 patients, randomized to the unilateral or bilateral approach, to have an 80% statistical power (alpha = 0.05, beta = 0.20) of detecting a difference between a 5% and a 10% risk of missing a tumor.

Adenoma↗
PubMed2005

Mathematical models for the control of cystic echinococcosis.

Cystic echinococcosis (CE) caused by Echinococcus granulosus is a global public health problem. In many areas the disease is being diagnosed in increasing numbers, whilst in other areas it is re-emerging due to the collapse of public health programmes associated with socio-economic changes. Mathematical models of the transmission dynamics between animals can have an important role to play in developing control options. In particular the parasite is highly endemic in many lower income countries where resources to undertake an intensive control programme that has been successful in wealthy countries, such as New Zealand, are not available. Data from dogs and livestock have been collected and modelled from a number of different countries and regions. In Australia and New Zealand transmission modelling was first developed and these models have been refined using data from the Middle East and central Asia. The model indicates that relatively intense anthelmintic treatment of the dog population will result in a substantial decrease in the parasite population over time and has been supported by the results of control programmes. However, if the newly developed sheep vaccine is included in the control programme, then it should be possible to treat dogs less frequently to achieve the same result. This is due to the potentiating effects of attacking the parasite at two places in its life cycle. This should result in considerable cost savings over the use intensive anthelmintic treatment as the sole method of control.

Animals↗
PubMed1995

Interpretation of serological surveillance data for measles using mathematical models: implications for vaccine strategy.

Serological surveillance of measles immunity has been carried out in England since 1986/7. Results from sera collected in 1989-91 revealed that the proportion of school age children who were susceptible to measles was increasing, following the introduction of the measles, mumps and rubella vaccination programme in October 1988. Mathematical models are used to interpret these data and determine whether this increasing susceptibility is sufficient to allow a resurgence of disease from the low levels achieved by 1993. The models summarize serological profiles by a single parameter, the reproduction number R, which quantifies the level of herd immunity in the population. Results showed that there was cause for concern over the levels of susceptibility to measles, with an epidemic of over 100,000 cases likely in 1995/6. These predictions are consistent with trends in the incidence and age distribution of measles and have enabled the planning of a major vaccination campaign.

Adolescent↗
PubMed2001

A mathematical model of rat cortical collecting duct: determinants of the transtubular potassium gradient.

In assessing disorders of potassium excretion, urine composition is used to calculate the transtubular gradient (TTKG), as an estimate of tubule fluid concentration, at a point when the fluid was last isotonic to plasma, namely, within the cortical collecting duct (CCD). A mathematical model of the CCD has been developed, consisting of principal cells and alpha- and beta-intercalated cells, and which includes Na(+), K(+), Cl(-), HCO, CO(2), H(2)CO(3), phosphate, ammonia, and urea. Parameters have been selected to achieve fluxes and permeabilities compatible with data obtained from perfusion studies of rat CCD under the influence of both antidiuretic hormone and mineralocorticoid. Both epithelial (flat sheet) and tubule models have been configured, and model calculations have focused on the determinants of the TTKG. Using the epithelial model, luminal K(+) concentrations can be computed at which K(+) secretion ceases (0-flux equilibrium), and this luminal concentration derives from the magnitude of principal cell peritubular uptake of K(+) via the Na-K-ATPase, relative to principal cell peritubular membrane K(+) permeability. When the model is configured as a tubule and examined in the context of conditions in vivo, osmotic equilibration of luminal fluid produces a doubling of the initial K(+) concentration, which, depending on delivered load, may be substantially greater than the zero-flux equilibrium value. Under such circumstances, the CCD will be a site for K(+) reabsorption, although the relatively low permeability ensures that this reabsorptive flux is likely to be small. Osmotic equilibration may also raise luminal NH(3) concentrations well above those in cortical blood. In this situation, diffusive reabsorption of NH(3) provides a mechanism for base reclamation without the metabolic cost of active proton secretion.

Acids↗
PubMed2000

Molecular biology of breast cancer metastasis. The use of mathematical models to determine relapse and to predict response to chemotherapy in breast cancer.

Breast cancer mortality rates have shown only modest improvement despite the advent of effective chemotherapeutic agents which have been administered to a large percentage of women with breast cancer. In an effort to improve breast cancer treatment strategies, a variety of mathematical models have been developed that describe the natural history of breast cancer and the effects of treatment on the cancer. These models help researchers to develop, quantify, and test various treatment hypotheses quickly and efficiently. The present review discusses several of these models, with a focus on how they have been used to predict the initiation time of metastatic growth, the effect of operative therapy on the growth of metastases, and the optimal administration strategy for chemotherapy.

Algorithms↗