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 685 records · Page 38Linked to original sources
PubMed1979

Myogenic microvascular responses to change of transmural pressure. A mathematical approach.

The recently described static and dynamic myogenic responses in the sympathectomized skeletal muscle microvessels to a given transmural pressure (PT) change applied at different rates (dPT/dt) (Grände & Mellander 1978), were further analysed in this study with a mathematical approach. The hypothesis that myogenic reactions are triggered by and related to wall tension was also tested. The mathematical model was based on a force-equilibrium in the microvessel wall including passive forces related to vascular transmural pressure, elasticity, and wall-viscosity, and active myogenic forces related to wall tension and its rate of change. Great resemblance was demonstrated between microvascular resistance curves obtained with the model and corresponding curves observed in vivo, indicating that the model quite adequately can describe myogenic microvascular resistance responses to transmural pressure stimuli. The results support the myogenic hypothesis in general and, in particular, the concept of an important rate-sensitivity in myogenic microvascular control and are compatible with the view that myogenic reactions are triggered by and related to change of wall tension. The model, in addition, provided data for certain microvascular variables which are difficult to assess by in vivo observations, e.g. Young's modulus of elasticity, wall tension, its rate of change, and internal vessel radius, and it offered a means to define more precisely the role of physical factors like effects of Poiseuille's and Laplace's laws in vascular resistance regulation.

Animals↗
PubMed1992

Re-examining repeated testing and teacher effects in a remedial mathematics course.

This study examined the impact of repeated testing and teachers' effects on student achievement in a remedial mathematics course. A 2 x 2 completely randomised factorial design was used, with final examination performance the dependent variable and testing attempts and the teacher factor the independent variables. The study found no main effects for teacher but a main effect for testing attempts and a teacher-factor/testing-attempt interaction. Post hoc findings qualified a direct interpretation of the main effect. The implications for further research and application are discussed, giving special attention to teacher effects, the needs of remedial mathematics instruction, and the claims of mastery-learning pedagogies.

Achievement↗
PubMed2001

A mathematical model for chemoattractant gradient sensing based on receptor-regulated membrane phospholipid signaling dynamics.

The crawling movement of cells in response to a chemoattractant gradient is a complex process requiring the coordination of various subcellular activities. Although a complete description of the mechanisms underlying cell movement remains elusive, the very first step of directional sensing, enabling the cell to perceive the imposed gradient, is becoming more transparent. A fundamental problem of directional sensing is its exquisite sensitivity. Even in the presence of relatively shallow chemoattractant gradients, cell projections are extended precisely in the region exposed to the highest chemoattractant concentration. This reflects the existence of a mechanism for amplifying the external signal. Recent experiments have identified a potential candidate for the seat of this amplification-membrane phosphoinositides such as PI4,5P2 and PI3,4,5P3 appear to be the first components of the signal transduction pathway to be amplified. Perturbing the cell with various chemoattractant gradients reveals a rich spectrum of phosphoinositide dynamics (Parent, C. A., and P. N. Devreotes. Science 284:765, 1999). The goal of this work is to develop a mathematical model of these phosphoinositide dynamics. Specifically, we address the following questions: (a) Which signaling pathway could lead to the localized accumulation of membrane phosphoinositides? (b) Why is this accumulation independent of the slope and mean value of the chemoattractant gradient? The model is based on the phosphoinositide cycle that transfers phosphoinositides between the plasma membrane and endoplasmic reticulum. We show that a mathematical model taking due account of receptor desensitization and the reaction-diffusion processes of the phosphoinositide cycle captures many of the experimentally observed dynamics. Having shown the plausibility of the model with respect to directional sensing, we discuss its implications for lamellipod extension, the process that follows directional sensing.

Biomedical Engineering↗
PubMed1991

New mathematical definition and calculation of axial rotation of anatomical joints.

In the field of joint kinematics, clinical terms such as internal-external, or medical-lateral, rotations are commonly used to express the rotation of a body segment about its own long axis. However, these terms are not defined in a strict mathematical sense. In this paper, a new mathematical definition of axial rotation is proposed and methods to calculate it from the measured Euler angles are given. The definition and methods to calculate it from the measured Euler angles are given. The definition is based on the integration of the component of the angular velocity vector projected onto the long axis of the body segment. First, the absolute axial rotation of a body segment with respect to the stationary coordinate system is defined. This definition is then generalized to give the relative axial rotation of one body segment with respect to the other body segment where the two segments are moving in the three-dimensional space. The well-known Codman's paradox is cited as an example to make clear the difference between the definition so far proposed by other researchers and the new one.

Biomechanical Phenomena↗
PubMed1999

Sources of mathematical thinking: behavioral and brain-imaging evidence.

Does the human capacity for mathematical intuition depend on linguistic competence or on visuo-spatial representations? A series of behavioral and brain-imaging experiments provides evidence for both sources. Exact arithmetic is acquired in a language-specific format, transfers poorly to a different language or to novel facts, and recruits networks involved in word-association processes. In contrast, approximate arithmetic shows language independence, relies on a sense of numerical magnitudes, and recruits bilateral areas of the parietal lobes involved in visuo-spatial processing. Mathematical intuition may emerge from the interplay of these brain systems.

Adult↗
PubMed1992

Determination of the mechanism of retrotransfer by mechanistic mathematical modeling.

Two mathematical models to elucidate the mechanism of retromobilization (or retrotransfer), that is, the ability of conjugative plasmids to mobilize genes into the cell containing the conjugative plasmid, were developed. This study deals with retromobilization of nonconjugative plasmids (Tra-Mob+). Plasmid transfer was modeled by two mass action models. The first is based on the hypothesis that retromobilization of the Tra-Mob+ vector occurs in one step, by means of the pilus formed by the Tra+ plasmid in the original host. In the second model, retromobilization is considered to be a two-step process involving two transfer events. The first step involves the transfer of the Tra+ plasmid from the recipient cell to the donor of the nonconjugative vector, and during the second encounter the nonconjugative vector is mobilized toward the recipient. Since the relationships between the number of transconjugants and the number of recipients for the two models are different, filter matings were performed for short time periods with different initial densities of the recipient population. Comparison of the numbers of transconjugants with the results of the mathematical equations confirmed the hypothesis that retromobilization is a one-step conjugation process.

Conjugation, Genetic↗
PubMed1980

Passage of molecules through the wall of the gastrointestinal tract. II. Application of low-molecular weight polyethyleneglycol and a deterministic mathematical model for determining intestinal permeability in man.

The intestinal permeability to low molecular weight polyethyleneglycol (PEG) has been evaluated by means of a simple mathematical model and computer-aided curve-fitting procedures. Macrogolum 400, a mixture of 11 PEGs with molecular weights ranging from 194 to 634 daltons, was taken together with a liquid meal and a six-hour portion of urine collected. The different PEGs were then extracted from the urine, separated from each other by gas-liquid chromatography, and the relative peak area of each individual PEG determined. The distribution of different PEGs in the urine was then compared with the original PEG-distribution in three different ways: (1) by comparing the median values of the molecular weights, (2) by comparing the mean and standard deviation after curve fitting to the normal distribution, and (3) by curve fitting to mathematical filter functions demonstrating molecular exclusion due to size. It thus appeared that molecules were excluded both in the high and in the low molecular weight range, possibly by a combined effect of the intestinal permeability barrier and an escape to other compartments than the urine. However, relatively more of the larger PEGs passed from the intestine to the urine in a patient with Crohn's disease than in an apparently healthy individual.

Adult↗
PubMed1998

Insulin secretion rates estimated by two mathematical methods in pancreas-kidney transplant recipients.

After pancreas-kidney transplantation, it is difficult to obtain an accurate estimate of the insulin secretion of the pancreas graft, since several pitfalls are involved using peripheral C-peptide and/or insulin measurements in this determination. In this study, the individual kinetic parameters of C-peptide and then the rates of insulin secretion were estimated by two mathematical methods, the deconvolution method and the "combined model" during slow (oral glucose) and fast (intravenous glucagon) changes in insulin secretion in six successful pancreas-kidney transplant recipients with systemic delivery of insulin (Px), six nondiabetic kidney-transplant recipients with portal insulin secretion (Kx), six nondiabetic controls (NS), and six C-peptide-negative insulin-dependent diabetes mellitus patients (IDDM). Decreased C-peptide clearance and basal and poststimulatory hyperinsulinemia were found in both Px and Kx compared with NS (P < 0.05). Similar glucose responses were observed after intravenous glucagon in all groups, whereas the responses after oral glucose were 30% higher in Px and Kx than in NS (P < 0.05). During oral glucose and after intravenous glucagon, both mathematical methods resulted in significantly lower maximal and incremental insulin secretion rates (ISR) in Px than in Kx (P < 0.05). In contrast, calculations of incremental ISR in NS and Px induced by the two beta-cell stimuli were about the same but significantly higher in Kx than in NS (P < 0.05). These results differed markedly from those obtained using peripheral measurements of insulin and C-peptide alone. In conclusion, when C-peptide clearance and insulin metabolism change, such as in pancreas-kidney transplant recipients, accurate evaluation of insulin secretion from the graft can be obtained only by using individual kinetics of the peptides before calculating the ISR. This study also clearly demonstrates that insulin secretion after pancreas transplantation is still defective.

Adult↗
PubMed1987

Profiles of water and solute transport along long-loop descending limb: analysis by mathematical model.

We simulated profiles of water and solute transport along the descending limb of the long-loop nephron by a mathematical model based on mass balance equations for water, sodium, potassium, and urea, using phenomenological coefficients reported for hamsters. We assumed that interstitial concentration of sodium, potassium, and urea increased linearly along the descending limb from 150 to 350, from 5 to 50, and from 5 to 300 mM, respectively. Under this condition an increase in osmolality at the end-descending limb was mainly accounted for by the absorption of water. Considerable amounts of potassium and urea were secreted along the descending limb. Sodium was reabsorbed rather than secreted along the descending limb by both diffusion and solvent drag. The secreted amounts of urea and potassium were comparable to those observed by micropuncture studies. The sodium concentration in the lumen was higher than in the interstitium, with the transmural sodium gradient being 15 meq/liter at the hairpin turn. The potassium mass flow rate at the end-descending limb increased by 2.4 times. Large variations in potassium concentration of the delivered fluid scarcely changed the potassium mass flow rate at the end-descending limb. The secretion of urea and potassium and the reabsorption of sodium were increased as a function of delivered flow rate. An increase in corticomedullary urea gradient decreased the net potassium secretion along the descending limb. When the transport parameters for rabbits were used, both reabsorption of sodium and addition of urea were decreased, but a similar amount of potassium was secreted. These analyses indicate that the mathematical model that takes the species difference and internephron heterogeneity into consideration is useful in illustrating the transport processes along the descending limb of Henle's loop under various physiological and pathophysiological conditions.

Biological Transport, Active↗
PubMed1997

Mathematical approach for estimating iron needs in hemodialysis patients on erythropoietin therapy.

Functional iron deficiency occurs when recombinant human erythropoietin (rHuEPO) accelerates erythropoiesis to an extent that the iron availability cannot meet the anticipated demand. Such a phenomenon will reduce the optimal response to rHuEPO. To estimate the iron needs of functional iron deficiency in hemodialysis patients on rHuEPO therapy, we utilized a mathematical method. Forty hemodialysis patients were examined in the study, and all had a baseline serum ferritin (SF) level > 100 microg/l. They were stratified into patients with a transferrin saturation (TfS) value > or = 25% (group I) and those below this value (group II). The treatment protocol consisted of rHuEPO therapy in the two groups for 6 months and iron supplement only in group II. The target hemoglobin level was 10.5 g/dl, and iron metabolism indices were analyzed prior to and following therapy. The results showed (1) in group I (n = 20) hemoglobin rose from 7.5 +/- 0.9 to 10.7 +/- 0.7 g/dl (p < 0.01) and the mean SF level declined from 1,583 +/- 997 to 968 +/- 664 mg (p < 0.01); (2) in group II (n = 20) hemoglobin also increased from 7.8 +/- 0.9 to 10.6 +/- 0.8 g/dl (p < 0.01) following iron supplement, while the SF rose from 183 +/- 70 to 326 +/- 125 mg (p < 0.01); (3) TfS was significantly elevated in group II following iron therapy (18.9 +/- 4.8 vs. 34.5 +/- 9.1%, p < 0.01), and (4) the nomogram showed a sensitivity of 80%, a specificity of 100%, a positive predictive value of 100%, and a negative predictive value of 83% in estimating the iron status before rHuEPO therapy. We conclude that SF levels reflect iron stores and that TfS < 25% is an index of functional iron deficiency. Iron supplementation is not necessary in patients with SF > 100 microg/l and TfS > or = 25%. It seems rational to provide intravenous iron in EPO-resistant patients with functional iron deficiency (SF > 100 microg/l, TfS < 25%). This paper illustrates the importance that accurate assessment of iron needs by a mathematical method would enhance treatment efficacy and avoid iron overload in hemodialysis patients on rHuEPO therapy.

Anemia↗
PubMed1996

Influence of cardiopulmonary disease on resolution of pulmonary embolism. A mathematical model to predict remaining defects at six months.

Recovery of lung perfusion after pulmonary embolism (PE) is conditioned by several factors. The aim of this study was to analyze the differences of reperfusion after PE between patients with and without preexisting cardiopulmonary disease, and to develop a mathematical model to predict, at diagnosis, the size of defects in lung perfusion scan at 6 months after treatment. We included 83 patients with diagnosis of PE in a non-concurrent cohort study (cohort I: 26 with preexisting cardiopulmonary disease, and cohort II: 57 without previous cardiopulmonary disease). Lung perfusion scan was performed at diagnosis, 7-10 days after treatment and at 6 months. The defect size was quantified following a numerical score. The recovery of perfusion after 7-10 days was 33% in cohort I and 45% in cohort II, and 50% and 72%, respectively, at the last control at 6 months. A multiple-regression analysis was performed using the final size of defects at 6 months (y) as the dependent variable, and the defect size at diagnosis (x) and the presence of preexisting cardiopulmonary disease (z) as independent variables. The regression equation was y = 1.29 + 0.15x + 2.98z. We conclude that: (1) in patients with cardiopulmonary diseases, the remaining defects at 6 months were larger; (2) at diagnosis, using a mathematical model, it is possible to predict the size of the defects in lung perfusion scan at 6 months in patients with or without previous cardiopulmonary disease.

Aged↗
PubMedDate not supplied

The quick machine--a mathematical model for the extrinsic activation of coagulation.

The present paper describes a mathematical model of the kinetics of the extrinsic coagulation cascade in vitro. The coagulation factors FI, FII, FV, FVII, FX, heparin and antithrombin III (ATIII) as well as soluble fibrin polymers are considered. The effect of single-factor deficiencies of the factors II, V, VII and X, diseases like hypo- and dysfibrinogenaemia, hepatic insufficiency, inhibited polymerisation by degradation products, heparin therapy with and without ATIII deficiency and coumarin therapy on prothrombin time can be portrayed. Physiology of coagulation is represented in a dynamic mathematical model as a differential equation system. The model is based on three reaction types: enzymatic cleavage, complex formation and polymerisation. The model was implemented in a continuous simulation program on a personal computer using the Pascal programming language. Unknown rate constants were estimated by chi 2 fit. Prothrombin time calculated by the model was compared to the training set of 20 plasma samples. In most but not all cases the model harmonized quite well with the coagulometric data.

Blood Coagulation↗
PubMed1980

Cross-sectional echocardiography. II. Analysis of mathematic models for quantifying volume of the formalin-fixed left ventricle.

Cross-sectional echocardiography was used to quantify volume in 21 canine left ventricles that were fixed in formalin and immersed in mineral oil. Area, length and diameter measurements were obtained from short- and long-axis cross-sectional images of the left ventricle and volume was calculated by seven mathematic models. Calculated volume was then compared, by linear regression and percent error analyses, with fluid volume of the left ventricle, obtained by filling the chamber with a known amount of fluid. Volumes ranged from 13-146 ml. Mathematic models using short-axis area and long-axis length gave higher correlation coefficients (r = 0.982 and r = 0.969) and lower mean errors (10-20%) than standard formulas previously used for M-mode echo and angiography. Thus, short-axis area analysis with cross-sectional echocardiography is well-suited for quantifying left ventricular volumes in dogs.

Animals↗
PubMed1996

Mathematical simulation of unidirectional tissue formation: in vitro transanastomotic endothelialization model.

In vitro transanastomotic endothelialization was studied using a mathematical model with the Fisher equation. The Fisher equation is a nonlinear parabolic equation which has a cell migration term and a population growth term. The mathematical model was used to simulate recent experiments performed to investigate quantitatively the unidirectional formation of a bovine endothelial cell monolayer in vitro. The two parameters included in the equation were estimated using a trial and error method in which the calculated solutions of the various values of the two parameters are compared with the experimental data and the best fit pair is adopted: one parameter, D, which represents the unidirectional cell migration rate and the other, k, which represents the population growth rate. The calculated solutions fit the experimental data well. We also simulated the healing of a mechanically disrupted endothelial monolayer sheet. The significance of cellular biomechanics in tissue formation and design of tissue-engineered devices is discussed.

Animals↗
PubMed1994

Mathematical coupling explains dependence of oxygen consumption on oxygen delivery in ARDS.

Because of potential for mathematical coupling of measurement errors in shared variables used to calculate oxygen consumption (FickVO2) and oxygen delivery (DO2), we asked whether determination of the FickVO2-DO2 relationship in individual patients with ARDS was statistically valid. We studied 17 clinically resuscitated patients with severe ARDS, measuring FickVO2, CalorimetricVO2 (using analysis of respiratory gases), and DO2 at regular intervals while DO2 was increased using an infusion of dobutamine. Overall, we found that DO2 (pre 482 +/- 143, post 616 +/- 170 ml O2/min.m2, p < 0.01) and FickVO2 (pre 130 +/- 23, post 147 +/- 24 ml O2/min.m2, p < 0.02) increased significantly with dobutamine infusion, but CalorimetricVO2 measured simultaneously did not change (pre 128 +/- 22, post 128 +/- 22 ml O2/min x m2, p = NS). In addition, unpooled weighted slope for FickVO2 versus DO2 (0.06) was significantly different from zero, but unpooled weighted slope for CalorimetricVO2 versus DO2 (0.01) was not significantly different from zero. Slopes of the FickVO2-DO2 relationship were significant for only three individual patients. Using methods by Stratton and colleagues to analyze the effect of mathematical coupling in the FickVO2-DO2 relationship, we found that in all patients the slope of measurement errors was greater than observed slope and that observed slope was greater than estimated true slope. Estimated true slope of the FickVO2-DO2 relationship in all individual patients was not significant. Therefore, we suggest that determination of the FickVO2-DO2 relationship in individual patients who are resuscitated and hemodynamically stable is most often not statistically significant.(ABSTRACT TRUNCATED AT 250 WORDS)

Adult↗
PubMedDate not supplied

A cross-sectional study of mathematics achievement, estimation skills, and academic self-perception in students of varying ability.

This study investigated students' mathematics achievement, estimation ability, use of estimation strategies, and academic self-perception. Students with learning disabilities (LD), average achievers, and intellectually gifted students (N = 135) in fourth, sixth, and eighth grade participated in the study. They were assessed to determine their mathematics achievement, ability to estimate discrete quantities, knowledge and use of estimation strategies, and perception of academic competence. The results indicated that the students with LD performed significantly lower than their peers on the math achievement measures, as expected, but viewed themselves to be as academically competent as the average achievers did. Students with LD and average achievers scored significantly lower than gifted students on all estimation measures, but they differed significantly from one another only on the estimation strategy use measure. Interestingly, even gifted students did not seem to have a well-developed understanding of estimation and, like the other students, did poorly on the first estimation measure. The accuracy of their estimates seemed to improve, however, when students were asked open-ended questions about the strategies they used to arrive at their estimates. Although students with LD did not differ from average achievers in their estimation accuracy, they used significantly fewer effective estimation strategies. Implications for instruction are discussed.

Achievement↗
PubMedDate not supplied

Strategy development in children with mathematical disabilities: insights from the choice/no-choice method and the chronological-age/ ability-level-match design.

This study investigated the strategy characteristics and development of children with mathematical disabilities (MD) in the domain of simple addition and subtraction, in terms of Lemaire and Siegler's model of strategic change, using the choice/no-choice method and the combined chronological-age (CA)/ability-level (AL)-match design. Four groups of children, matched on either CA or mathematical AL, solved a series of 36 problems with the bridge over 10 in four conditions. In the choice condition, children could choose between retrieval, decomposition to 10, and counting on to solve each problem. In the retrieval, decomposition, and counting conditions, they had to answer the same 36 problems using retrieval, decomposition to 10, and counting on, respectively. The results revealed clear differences in the frequency, efficiency, and adaptiveness with which the CA-matched children applied the available strategies. In contrast, we observed no differences in strategy frequency, efficiency, and adaptiveness between the AL-matched children. These results support the hypothesis that the strategy development of children with MD is marked by a delay rather than a specific deficit. Moreover, this study further documents the value of the methodology used to study children's strategy use and development in the domain of simple arithmetic.

Age Factors↗
PubMed1989

Cross-sectional comparisons of the mathematical performance of children with learning disabilities: are we on the right track toward comprehensive programming?

This study examines the mathematical performance of 220 children from 8 years through 17 years of age diagnosed as having learning disabilities. Student records were searched for data indicating performance on standardized test instruments relating to mathematics. Data for the Woodcock-Johnson Psycho-Educational Achievement Battery math subtests and for the IQ scores from the Wechsler Intelligence Scale for Children-Revised were obtained. Comparisons were made among children at different ages and among specific age clusters. Primary attention was directed toward calculations and applications of math concepts and principles. Developmental patterns across the ages studied were discovered. Implications for long-term comprehensive programming are presented.

Achievement↗