Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “MATHEMATICS”

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 1,801 records · Page 100Linked to original sources

Cancer immunotherapy by interleukin-21: potential treatment strategies evaluated in a mathematical model.

The newly characterized interleukin (IL)-21 plays a central role in the transition from innate immunity to adaptive immunity and shows substantial tumor regression in mice. IL-21 is now developed as a cancer immunotherapeutic drug, but conditions for efficacious therapy, and the conflicting immunostimulatory and immunoinhibitory influence of the cytokine, are yet to be defined. We studied the effects of IL-21 on tumor eradication in a mathematical model focusing on natural killer (NK) cell-mediated and CD8+ T-cell-mediated lysis of tumor cells. Model parameters were estimated using results in tumor-bearing mice treated with IL-21 via cytokine gene therapy (CGT), hydrodynamics-based gene delivery (HGD), or standard interval dosing (SID). Our model accurately retrieved experimental growth dynamics in the nonimmunogenic B16 melanoma and the immunogenic MethA and MCA205 fibrosarcomas, showing a strong dependence of the NK-cell/CD8+ T-cell balance on tumor immunogenicity. Moreover, in melanoma, simulations of CGT-like dosing regimens, dynamically determined according to tumor mass changes, resulted in efficient disease elimination. In contrast, in fibrosarcoma, such a strategy was not superior to that of fixed dosing regimens, HGD or SID. Our model supports clinical use of IL-21 as a potent stimulator of cellular immunity against cancer, and suggests selecting the immunotherapy strategy according to tumor immunogenicity. Nonimmunogenic tumors, but not highly immunogenic tumors, should be controlled by IL-21 dosing, which depends on tumor mass at the time of administration. This method imitates, yet amplifies, the natural anticancer immune response rather than accelerates only one of the response arms in an unbalanced manner.

Animals↗

Use of the Hagen-Poiseuille law: a new mathematical approach for the integration and evaluation of anorectal physiological testing in patients with faecal incontinence and pelvic dyschezia and in normal controls.

This work was done in order to study the possibility of using the Hagen-Poiseuille law for flow of fluids through tubes to integrate and quantitate the anorectal physiological parameters in patients suffering from faecal incontinence and functional pelvic outlet obstruction compared to normal controls. The Hagen-Poiseuille law was intended to be used in the explanation of the role played by different sensory and motor functions of the anorectal segment in maintaining continence and normal rectal evacuation. The intrarectal pressures during rest, coughing, attempted defaecation, rectal sensation, and rectal compliance at the point of first rectal sensation were measured using anorectal manometry. Anal canal length and diameter were measured using lateral defaecographic views during rest, squeeze, and attempted defaecation, and the anal sphincteric reflex contraction in response to coughing or Valsalva's manoeuver was measured using plug or needle electromyography. These factors were analyzed using the Hagen-Poiseuille law in order to determine anal canal resistance and flow to air, water, and BaSO4 during rest, coughing, and attempted defaecation in controls, during attempted defaecation in patients with functional pelvic outlet obstruction, and during rest and coughing in patients with faecal incontinence. The Hagen-Poiseuille law could detect anal continence in all controls and could also detect and quantitate functional pelvic dyschezia in all patients. The equation could detect and quantitate faecal incontinence in 8 of 14 patients (57.14%) during rest, in 11 of 14 (78.57%) during coughing, and in all 14 patients after correction for sensory and reflex deficits. Both the Hagen-Poiseuille law and the law of Laplace and their proposed hybrid law were successful in explaining some facts concerning factors affecting normal continence and defaecation. The Hagen-Poiseuille law is a useful new mathematical approach for the integration and quantitation of normal and abnormal continence and defaecation. It can be used to plan for treatment and to determine the outcome of patients suffering from functional anorectal disease.

Adolescent↗

Insights from mathematical modeling of renal tubular function.

Mathematical models of proximal tubule have been developed which represent the important solute species within the constraints of known cytosolic concentrations, transport fluxes, and overall epithelial permeabilities. In general, model simulations have been used to assess the quantitative feasibility of what appear to be qualitatively plausible mechanisms, or alternatively, to identify incomplete rationalization of experimental observations. The examples considered include: (1) proximal water reabsorption, for which the lateral interspace is a locus for solute-solvent coupling; (2) ammonia secretion, for which the issue is prioritizing driving forces - transport on the Na+/H+ exchanger, on the Na,K-ATPase, or ammoniagenesis; (3) formate-stimulated NaCl reabsorption, for which simple addition of a luminal membrane chloride/formate exchanger fails to represent experimental observation, and (4) balancing luminal entry and peritubular exit, in which ATP-dependent peritubular K+ channels have been implicated, but appear unable to account for the bulk of proximal tubule cell volume homeostasis.

Ammonia↗

Solute transport in continuous arteriovenous hemodiafiltration: a new mathematical model applied to clinical data.

A mathematical model of continuous arteriovenous hemodiafiltration is presented, by which the diffusive mass transfer coefficient (Kd) for a solute may be calculated from blood, filtrate and dialysate flow rates and solute concentrations. The model was applied to clinical data obtained with 0.6-m2 AN69 capillary dialyzers that had been used for up to 5 days. The diffusive mass transfer coefficient proved to depend on dialysate flow rate. Furthermore, it was related to the membrane index of ultrafiltration, as measured in the clinic, and to the filter resistance to blood flow. Measurement of these filter characteristics allowed a reasonable prediction of solute clearance.

Data Interpretation, Statistical↗

Two new pulmonary functional indexes suggested by a simple mathematical model.

We propose a new experiment consisting of several 'single-breath' tests made during different stages of nitrogen (or other inert gas) washouts and then measuring the slope of the alveolar plateau divided by the mean expiratory nitrogen concentration (normalized slope). A simple mathematical analysis predicts that: (a) The normalized slope should grow in function of the breath number n (after the beginning of the washout) chosen to perform the single breath test. It should reach an asymptotic value which is an index of the asynchroism of the expiratory movement (sequential ventilation): Isv. (b) The index of the distribution of the ventilation (IDV) is not the slope of the alveolar plateau as usually considered, but the slope of the normalized slope of the alveolar plateau plotted in function of n and divided by ISV.

Breath Tests↗

A mathematical model of coagulation factor VIII kinetics.

It appears that the binding of coagulation factor VIII to von Willebrand factor in plasma stabilizes the otherwise highly labile factor VIII. A mathematical model of factor VIII kinetics has been developed based upon this proposed effect of factor VIII binding. The model's kinetic parameter values have been estimated by fitting the model to data available in the medical literature. The model gives accurate quantitative predictions of the elevated steady-state concentrations of factor VIII in clinical conditions associated with the acute phase reaction and in pregnancy, the decreased steady-state concentrations of factor VIII in females heterozygous for hemophilia, the decreased steady-state concentrations of factor VIII in patients with type 1 (heterozygous) and type 3 (homozygous) von Willebrand disease, and the variable half-life of factor VIII in factor replacement therapy for hemophilia and von Willebrand disease.

Computer Simulation↗

Human fetal weight and placental weight growth curves. A mathematical analysis from a population at sea level.

A mathematical analysis of human fetal and placental growth curves was made on data collected prospectively from a population at sea level. Both the fetal and placental growth curves can best be described by a form of the logistic equation inhibited growth model. The fetal growth rate reaches its maximum approximately 4 weeks after the placental growth rate has reached its maximum. Growth rate constants were calculated for several populations at various altitudes.

Altitude↗

Mathematical models for fetal growth: application for biparietal diameter measurement.

Evaluation of the adequacy of fetal growth by measurements of fetal size required theoretical formulae for the assessment of present size from previous measurements. The various models presented in the literature assume the same mathematical formula for the whole pregnancy. In this study, a model of different polynomial approximations for the early and late stages of the pregnancy is compared to two models which assume a single formula for both stages of the pregnancy. The standard error of estimate is lower for the sectioned model.

Embryonic and Fetal Development↗

Cross-sectional echocardiography. I. Analysis of mathematic models for quantifying mass of the left ventricle in dogs.

Cross-sectional echocardiography was used to quantify left ventricular mass noninvasively in 21 dogs. Short- and long-axis cross-sectional images of the left ventricle were reproducibly traced at endocardial and epicardial borders during stop-motion video-tape replay. We used area, length and diameter measurements to calculate left ventricular mass by seven mathematic models, including the standard formulas used with M-mode echocardiography and cineangiography. Calculated mass was compared with excised weight of the left ventricle by regression and percent error analyses. Formulas using short-axis areas and long-axis length resulted in higher correlation coefficients (0.94--0.95) and lower mean errors (6--7%) than for standard formulas. Since short-axis areas account for regional left ventricular irregularities, noninvasive quantification of left ventricular mass by cross-sectional echocardiography in dogs is most accurate with formulas using short-axis areas.

Animals↗

Noninvasive quantification of regional myocardial perfusion with rubidium-82 and positron emission tomography. Exploration of a mathematical model.

Positron emission tomography (PET) centers without cyclotrons use generator-produced rubidium-82 (82Rb) for assessment of myocardial perfusion. The aim of the present study was to determine whether myocardial blood flow could be assessed quantitatively with 82Rb and PET. Because the myocardial extraction fraction of 82Rb varies inversely and nonlinearly with flow and cannot be measured conveniently with PET, we used an experimentally derived mathematical function defining the relation between single-pass extraction fraction of 82Rb and flow to obviate the necessity of measuring the extraction fraction directly. Myocardial blood flow in absolute terms (ml/g/min) was estimated from dynamic PET scans after intravenous administration of 82Rb in intact dogs and compared with flows measured with radiolabeled microspheres. In 36 comparisons in 13 dogs studied at rest, or after coronary occlusion, reperfusion, or after coronary hyperemia induced with intravenous dipyridamole, over the flow range from 0.2 to 2.0 ml/g/min, estimates of perfusion with rubidium correlated well with flows measured concomitantly with microspheres, although there was a slight underestimation of flow with rubidium (flow by 82Rb = 0.92 x flow by microspheres-0.021, r = 0.83). In general, estimates of flow in ischemic regions were less reliable than estimates for regions with normal flow. Thus, although the relation between myocardial extraction and retention of 82Rb and flow can vary under a variety of physiological and pathophysiological conditions, this study demonstrates the ability to obtain quantitative estimates of myocardial blood flow with 82Rb and PET under carefully defined conditions without measuring the extraction fraction directly.

Animals↗

Dynamic interactions and mutual synchronization of sinoatrial node pacemaker cells. A mathematical model.

Dynamic interactions and mutual entrainment of coupled sinoatrial pacemaker cells with different intrinsic frequencies were investigated using a computerized mathematical model. Transmembrane potentials were simulated using equations of individual membrane currents based on voltage clamp data for the sinoatrial node. The intrinsic frequency of a given cell was altered by applying bias hyperpolarizing current, or by changing the amount of slow inward current. Cells were coupled through simple ohmic resistances to form linear arrays of two or more cells. Simulations closely reproduced previous experimental work showing that the mutual interactions between pacemakers are mediated electrotonically and show phase dependence. Results from the present simulations provide an explanation for the ionic basis of these phase-dependent interactions. In addition, it is demonstrated that the mutual entrainment of coupled pacemakers can lead to their coordinated behavior (synchronization). Two pacemaker cells can synchronize at simple harmonic (i.e., 1:1, 2:1, etc.) or more complex ratios (3:2, 5:3, etc.), depending on the differences in intrinsic frequencies and the degree of electrical coupling between cells. Simulations using larger numbers of linearly connected cells yielded various patterns of pacemaker activity including 2:1 sinoatrial block and complex dysrhythmic activity. The overall results may be used to predict higher order interactions of thousands of cells comprising the sinus node. Under such a scheme, synchronization occurs not by the conducted influence of a dominant pacemaker cell, but by the mutual "democratic" interaction of individual pacemaker cells.

Action Potentials↗

Dynamics of encoding in neuron populations: some general mathematical features.

The use of a population dynamics approach promises efficient simulation of large assemblages of neurons. Depending on the issues addressed and the degree of realism incorporated in the simulated neurons, a wide range of different population dynamics formulations can be appropriate. Here we present a common mathematical structure that these various formulations share and that implies dynamical behaviors that they have in common. This underlying structure serves as a guide toward efficient means of simulation. As an example, we derive the general population firing-rate frequency-response and show how it may be used effectively to address a broad range of interacting-population response and stability problems. A few specific cases will be worked out. A summary of this work appears at the end, before the appendix.

Cerebral Cortex↗

Competition for neurotrophic factors: mathematical analysis.

Neurotrophic factors, particularly the neurotrophin gene family of neurotrophic factors, are implicated in activity-dependent anatomical plasticity in the visual cortex and at the neuromuscular junction. Accumulating evidence implicates neurotrophic factors as possible mediators of activity-dependent competition between afferents, leading to the segregation of afferents' arbors on the target space. We present a biologically plausible mathematical model of competition for neurotrophic factors. We show that the model leads to anatomical segregation, provided that the levels of neurotrophic factors released in an activity-independent manner, or the levels available by exogenous infusion, are below a critical value, which we derive. Above this critical value, afferent segregation breaks down. We also show that the model segregates afferents even in the presence of very highly correlated patterns of afferent activity. The model is therefore ideally suited for application to the development of ocular dominance columns in the kitten visual cortex.

Afferent Pathways↗

Mathematical expression of the effects of changes in body size on pulmonary function and structure.

The biological meaning of the mass coefficient "a" and mass exponent "b" of the power function relating body mass "M" and a morphometric or physiologic variable "y" is discussed (y = aMb). The mass coefficient represents the effect of intensive or qualitative factors on the considered function or structure. The theoretical mass exponent is a criterion for the constancy of the mass coefficient and the qualitative sameness of the compared animals. The Theory of Homomorphism shows that the power function is a mathematical-physical model for analyzing structure and function in animals of different size.

Animals↗

The effect of Pendelluft and dead space on nitrogen clearance: mathematical and experimental models and their application to the study of the distribution of ventilation.

Reinspired mixed dead space gas and Pendelluft may be considered to be part of a single process of interalveolar gas transfer. The effect of interalveolar gas transfer on nitrogen clearance from a two chamber lung model can be described by a single set of equations which hold for synchronous, and series ventilation. Interalveolar gas transfer may theoretically be either bidirectional or unidirectional. Bidirectional transfer results in an underestimation of the effective ventilation and volume of the well-ventilated compartment when nitrogen washout is analyzed by available methods. The volume of the poorly ventilated compartment is overestimated and its effective ventilation is usually overestimated but may be correctly or underestimated as distribution becomes more uneven. Unidirectional transfer has the same qualitative effect except that the ventilation of the poorly ventilated space is always overestimated. The distortions produced by both types of gas transfer become less marked as ventilation becomes more uneven.Nitrogen washout data from a model consisting of two rubber balloons connected with a Y tube agree well with the mathematical predictions. Application of the theory to data obtained from patients with advanced chronic obstructive lung disease suggests that estimates of the functional residual capacity and of the volume and ventilation of the poorly ventilated spaces are not greatly affected by interalveolar gas transfer when nitrogen washout is analyzed by usual methods.

Adult↗

A mathematical model of the volume, pH, and ion content regulation in reticulocytes. Application to the pathophysiology of sickle cell dehydration.

We developed a mathematical model of the reticulocyte, seeking to explain how a cell with similar volume but much higher ionic traffic than the mature red cell (RBC) regulates its volume, pH, and ion content in physiological and abnormal conditions. Analysis of the fluxbalance required by reticulocytes to conserve volume and composition predicted the existence of previously unsuspected Na(+)-dependent Cl- entry mechanisms. Unlike mature RBCs, reticulocytes did not tend to return to their original state after brief perturbations. The model predicted hysteresis and drift in cell pH, volume, and ion contents after transient alterations in membrane permeability or medium composition; irreversible cell dehydration could thus occur by brief K+ permeabilization, transient medium acidification, or the replacement of external Na+ with an impermeant cation. Both the hysteresis and drift after perturbations were shown to depend on the pHi dependence of the K:Cl cotransport, a major reticulocyte transporter. This behavior suggested a novel mechanism for the generation of irreversibly sickled cells directly from reticulocytes, rather than in a stepwise, progressive manner from discocytes. Experimental tests of the model's predictions and the hypothesis are described in the following paper.

Anemia, Sickle Cell↗

The mathematical basis of multivariate risk screening: with special reference to screening for Down's syndrome associated pregnancy.

The underlying mathematical techniques behind the multivariate normal distribution are explained in principle and expanded in detail for up to three variables. The application of multivariate distributions to screening programs is described with particular reference to the calculation of risk ratios for the detection of Down's syndrome between 15 and 19 weeks of gestation.

Adolescent↗

A comparison of two approaches for teaching complex, authentic mathematics problems to adolescents in remedial math classes.

Two groups of adolescents with learning difficulties in mathematics were compared on their ability to generate solutions to a contextualized problem after being taught problem-solving skills under two conditions, one involving standard word problems, the other involving a contextualized problem on videodisc. All problems focused on adding and subtracting fractions in relation to money and linear measurement. Both groups of students improved their performance on solving word problems, but students in the contextualized problem group did significantly better on the contextualized problem posttest and were able to use their skills in two transfer tasks that followed instruction.

Adolescent↗

Refine your search to explore more results.