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PubMed1992

Mathematical description of the concentration of oxytetracycline and penicillin-G in tissue cages in calves as related to the serum concentration.

A mathematical model based on Fick's laws of diffusion describing the concentration of drug in tissue cage models was elaborated. The model takes into account differences in protein binding, tissue cage geometry and serum pharmacokinetics. The validity of the model was tested against experimental data obtained from a tissue cage model in calves by simultaneous fitting to serum and tissue cage fluid (TCF) data in a non-linear least-squares regression computer program. Concentrations of penicillin-G (pen-G) in serum and TCF following intravenous (i.v.) administration of potassium pen-G were adequately described by the mathematical model. Concentrations in TCF after intramuscular (i.m.) administration of the same drug and of procaine pen-G could be predicted by the mathematical model. Concentrations of oxytetracycline (OTC) in serum and TCF following i.v. administration and continuous i.v. infusions were also adequately described by the model, and TCF concentrations after i.m. administration of the same drug could be roughly predicted. The results indicate that pen-G and OTC have the same permeability coefficient for transport from serum to TCF.

Animals↗
PubMed1975

Entry to medical schools with 'A' level in mathematics rather than biology.

The majority of British medical schools now accept for their shortest courses students who have mathematics at A level in place of the former requirement of biology A level. Only a small fraction of the entry, less than one-fifth, enters this way, in spite of statements by most medical schools that they make no distinction between those with mathematics and those with biology when making conditional offers of places. There is no evidence that those without biology are at a disadvantage in the courses. If the prospects of entry without A level biology were better publicized medical schools would have a wider field of possibly abler entrants, and pupils entering sixth forms could defer for a year a choice between a medical (or dental) career and one involving physical science, engineering, or other mathematics-based university education.

Biology↗
PubMed2002

Late potential analysis: is a mathematically-derived X,Y,Z lead system comparable to a true orthogonal X,Y,Z lead system?

BACKGROUND: Analysis of ventricular late potentials (LP) with signal-averaged ECG (SAECG) using three bipolar, orthogonal X,Y, Z leads is a validated method of risk-stratification in patients prone to ventricular tachycardia. The aim of this study was to validate a ECG system, which allows LP analysis using X,Y, Z leads mathematically derived from the standard 12-lead ECG. METHODS AND RESULTS: In 36 patients (age 56 +/- 12 years, coronary artery disease 71%, LVEF 46 +/- 14%) with known or suspected ventricular tachyarrhythmia, two consecutive SAECGs were recorded, one with mathematically derived and another one with true X,Y, Z leads. Time domain measurements with these different lead systems were compared using linear regression analysis and "Bland-Altman" plots. Correlation was good (r = 0.92) for the filtered QRS complex duration, but poor for the terminal QRS amplitude (RMS) and duration (LAS) criteria (r = 0.66 and 0.61, respectively; P < 0.0001). Defining LPS as present if at least two of the three time domain criteria were abnormal, the result matched in 28 (78%), but differed in 8 (22%) patients. CONCLUSION: SAECG using X,Y, Z leads mathematically derived from the standard 12-lead ECG compared to true bipolar X,Y, Z leads show a close correlation in filtered QRS duration, but can differ considerably in the other time domain measurements, resulting in different interpretation of LP analysis in 22%. Therefore, SAECG registration should currently be performed with true X,Y, Z leads, until the accuracy of other approaches is validated.

Adult↗
PubMed1998

Curriculum integration in nutrition and mathematics.

Today's school-aged children face a multitude of health issues that affect their well-being and academic performance. Partnerships have developed between health and education agencies to help American children succeed at math and science and to prepare them to make healthful, lifelong decisions. Curriculum integration provides a framework for children to apply knowledge from several disciplines and to use this knowledge to solve real-life problems at work and at play. Goals for instruction focus on the needs not only of the individual but also of society. Nutrition science and mathematics form a natural partnership. Nutrition science incorporates numerous mathematical concepts and procedures such as sorting, classifying, statistics, probability, estimation, and rates and proportion. In preparation for participation in a global and technological society that will require citizens to be quantitative thinkers, educators must endeavor to assist all children in becoming adults who are mathematically literate and competent.

Adolescent↗
PubMed2004

Uses and abuses of mathematics in biology.

In the physical sciences, mathematical theory and experimental investigation have always marched together. Mathematics has been less intrusive in the life sciences, possibly because they have until recently been largely descriptive, lacking the invariance principles and fundamental natural constants of physics. Increasingly in recent decades, however, mathematics has become pervasive in biology, taking many different forms: statistics in experimental design; pattern seeking in bioinformatics; models in evolution, ecology, and epidemiology; and much else. I offer an opinionated overview of such uses--and abuses.

Allergy and Immunology↗
PubMed2004

Introductory science and mathematics education for 21st-Century biologists.

Galileo wrote that "the book of nature is written in the language of mathematics"; his quantitative approach to understanding the natural world arguably marks the beginning of modern science. Nearly 400 years later, the fragmented teaching of science in our universities still leaves biology outside the quantitative and mathematical culture that has come to define the physical sciences and engineering. This strikes us as particularly inopportune at a time when opportunities for quantitative thinking about biological systems are exploding. We propose that a way out of this dilemma is a unified introductory science curriculum that fully incorporates mathematics and quantitative thinking.

Biological Science Disciplines↗
PubMed1980

Sex differences in mathematical ability: fact or artifact?

A substantial sex difference in mathematical reasoning ability (score on the mathematics test of the Scholastic Aptitude Test) in favor of boys was found in a study of 9927 intellectually gifted junior high school students. Our data contradict the hypothesis that differential course-taking accounts for observed sex differences in mathematical ability, but support the hypothesis that these differences are somewhat increased by environmental influences.

Adolescent↗
PubMed1994

Mathematical analysis and experiment on the corneal reflex test in spectacle wearers.

An experimental study and mathematical analysis of the corneal reflex test was undertaken in spectacle wearers. In the experimental study, photographs were taken of the corneal reflex through spectacles and the conversion ratios determined as measured in degrees/mm. In the mathematical analysis, the magnification effect of the lens was elucidated by three methods: geometrical analysis; real measurement of magnification factor; and ray tracing analysis. The real measurement of the conversion ratios was in good agreement with the conversion ratios determined by the three mathematical analyses. These results clearly showed that the corneal reflex test can be clinically useful even in wearers of spectacles.

Blinking↗
PubMed2006

Multipolar radiofrequency ablation with internally cooled electrodes: experimental study in ex vivo bovine liver with mathematic modeling.

PURPOSE: To evaluate the size and geometry of thermally induced coagulation by using multipolar radiofrequency (RF) ablation and to determine a mathematic model to predict coagulation volume. MATERIALS AND METHODS: Multipolar RF ablations (n = 80) were performed in ex vivo bovine livers by using three internally cooled bipolar applicators with two electrodes on the same shaft. Applicators were placed in a triangular array (spacing, 2-5 cm) and were activated in multipolar mode (power output, 75-225 W). The size and geometry of the coagulation zone, together with ablation time, were assessed. Mathematic functions were fitted, and the goodness of fit was assessed by using r(2). RESULTS: Coagulation volume, short-axis diameter, and ablation time were dependent on power output and applicator distance. The maximum zone of coagulation (volume, 324 cm(3); short-axis diameter, 8.4 cm; ablation time, 193 min) was induced with a power output of 75 W at an applicator distance of 5 cm. Coagulation volume and ablation time decreased as power output increased. Power outputs of 100-125 W at applicator distances of 2-4 cm led to a reasonable compromise between coagulation volume and ablation time. At 2 cm (100 W), coagulation volume, short-axis diameter, and ablation time were 66 cm(3), 4.5 cm, and 19 min, respectively; at 3 cm (100 W), 90 cm(3), 5.2 cm, and 22 min, respectively; at 4 cm (100 W), 132 cm(3), 6.1 cm, and 27 min, respectively; at 2 cm (125 W), 56 cm(3), 4.2 cm, and 9 min, respectively; at 3 cm (125 W), 73 cm(3), 4.9 cm, and 12 min, respectively; and at 4 cm (125 W), 103 cm(3), 5.5 cm, and 16 min, respectively. At applicator distances of 4 cm (>125 W) and 5 cm (>100 W), the zones of coagulation were not confluent. Coagulation volume (r(2) = 0.80) and RF ablation time (r(2) = 0.93) were determined by using the mathematic model. CONCLUSION: Multipolar RF ablation with three bipolar applicators may produce large volumes of confluent coagulation ex vivo. A compromise is necessary between prolonged RF ablations at lower power outputs, which produce larger volumes of coagulation, and faster RF ablations at higher power outputs, which produce smaller volumes of coagulation.

Animals↗
PubMed2002

Time-dependent transients in an ionically based mathematical model of the canine atrial action potential.

Ionically based cardiac action potential (AP) models are based on equations with singular Jacobians and display time-dependent AP and ionic changes (transients), which may be due to this mathematical limitation. The present study evaluated transients during long-term simulated activity in a mathematical model of the canine atrial AP. Stimulus current assignment to a specific ionic species contributed to stability. Ionic concentrations were least disturbed with the K(+) stimulus current. All parameters stabilized within 6-7 h. Inward rectifier, Na(+)/Ca(2+) exchanger, L-type Ca(2+), and Na(+)-Cl(-) cotransporter currents made the greatest contributions to stabilization of intracellular [K(+)], [Na(+)], [Ca(2+)], and [Cl(-)], respectively. Time-dependent AP shortening was largely due to the outward shift of Na(+)/Ca(2+) exchange related to intracellular Na(+) (Na) accumulation. AP duration (APD) reached a steady state after approximately 40 min. AP transients also occurred in canine atrial preparations, with the APD decreasing by approximately 10 ms over 35 min, compared with approximately 27 ms in the model. We conclude that model APD and ionic transients stabilize with the appropriate stimulus current assignment and that the mathematical limitation of equation singularity does not preclude meaningful long-term simulations. The model agrees qualitatively with experimental observations, but quantitative discrepancies highlight limitations of long-term model simulations.

Action Potentials↗
PubMed2002

A mathematical model of phase 2 reentry: role of L-type Ca current.

Phase 2 reentry (P2R) is known to be one of the mechanisms of malignant ventricular arrhythmias, especially those associated with Brugada syndrome. However, little is known about the underlying mechanism for P2R. Our aim in this study was to simulate P2R in a mathematical model to enable us to understand its mechanism and identify a potential therapeutic target. A mathematical model of the L-type Ca current was composed according to whole cell current data from guinea pig ventricular myocytes recorded at 37 degrees C. Our mathematical model was incorporated into the modified Luo-Rudy phase 2 model. We set a dispersion in transient outward current (I(to)) density within the theoretical fiber, composed of 80 serially arranged epicardial cells with gap junctions and then observed the P2R. The dispersion in I(to) density within an only 0.8-cm epicardial theoretical fiber generated P2R with our Ca channel but not with the original model. When the P2R developed in the theoretical fiber, the calculated extracellular field potential showed coved-type ST segment elevation. We succeeded in generating P2R in our model for the first time. The local epicardial P2R may contribute the genesis of coved-type ST segment elevation in the Brugada syndrome.

Action Potentials↗
PubMed1992

Intrinsic PEEP monitored in the ventilated ARDS patient with a mathematical method.

Under mechanical volume-controlled ventilation, the intensive care patient can develop intrinsic positive end-expiratory pressure (iPEEP); that is, the passive expiration is terminated by the following inspiration before the alveolar pressure comes to its physical equilibrium value. We present a mathematical method to estimate this alveolar dynamic iPEEP breath by breath, without the need of a maneuver. We tested it in paralyzed patients ventilated for adult respiratory distress syndrome after multiple trauma and/or sepsis, and we compared the results obtained with the new mathematical method with those from the occlusion method introduced by Pepe and Marini. The results agreed well (median difference of 0.8 mbar in 201 investigations in 12 patients). However, the mathematically determined values, representing dynamic iPEEP, are systematically slightly smaller than those measured by the occlusion maneuver. A variation of expiratory time suggests that this difference might be due to mechanical time-constant inhomogeneity, viscoelastic processes, or other mechanisms showing time dependence.

Adult↗
PubMed2005

Predicting human chronically paralyzed muscle force: a comparison of three mathematical models.

Chronic spinal cord injury (SCI) induces detrimental musculoskeletal adaptations that adversely affect health status, ranging from muscle paralysis and skin ulcerations to osteoporosis. SCI rehabilitative efforts may increasingly focus on preserving the integrity of paralyzed extremities to maximize health quality using electrical stimulation for isometric training and/or functional activities. Subject-specific mathematical muscle models could prove valuable for predicting the forces necessary to achieve therapeutic loading conditions in individuals with paralyzed limbs. Although numerous muscle models are available, three modeling approaches were chosen that can accommodate a variety of stimulation input patterns. To our knowledge, no direct comparisons between models using paralyzed muscle have been reported. The three models include 1) a simple second-order linear model with three parameters and 2) two six-parameter nonlinear models (a second-order nonlinear model and a Hill-derived nonlinear model). Soleus muscle forces from four individuals with complete, chronic SCI were used to optimize each model's parameters (using an increasing and decreasing frequency ramp) and to assess the models' predictive accuracies for constant and variable (doublet) stimulation trains at 5, 10, and 20 Hz in each individual. Despite the large differences in modeling approaches, the mean predicted force errors differed only moderately (8-15% error; P=0.0042), suggesting physiological force can be adequately represented by multiple mathematical constructs. The two nonlinear models predicted specific force characteristics better than the linear model in nearly all stimulation conditions, with minimal differences between the two nonlinear models. Either nonlinear mathematical model can provide reasonable force estimates; individual application needs may dictate the preferred modeling strategy.

Adult↗
PubMed1999

Predicting epistasis from mathematical models.

Classically, epistasis is either computed exactly by Walsh coefficients or estimated by sampling. Exact computation is usually of theoretical interest since the computation typically grows exponentially with the number of bits in the domain. Given an evaluation function, epistasis also can be estimated by sampling. However this approach gives us little insight into the origin of the epistasis and is prone to sampling error. This paper presents theorems establishing the bounds of epistasis for problems that can be stated as mathematical expressions. This leads to substantial computational savings for bounding the difficulty of a problem. Furthermore, working with these theorems in a mathematical context, one can gain insight into the mathematical origins of epistasis and how a problem's epistasis might be reduced. We present several new measures for epistasis and give empirical evidence and examples to demonstrate the application of the theorems. In particular, we show that some functions display "parity" such that by picking a well-defined representation, all Walsh coefficients of either odd or even index become zero, thereby reducing the nonlinearity of the function.

Algorithms↗
PubMed1980

Lewis Carroll: a study of mathematical inhibition.

Carroll's mathematical abilities appear to have been severely constrained--subject simultaneously to inhibition and distortion. Through an analysis of his informal commentary on his relation to mathematical puzzles I have attempted to understand and explain the nature of these inhibitions and distortions. Particular attention to his metaphor of the "mental bun," and his use of this metaphor, has led me to conclude that the mathematical puzzle served, for Carroll, distinctly fetishistic functions. This interpretation dovetails with Greenacre's early intuition about the prevalence in his literary work of fantasies and preoccupations reminescent of clinical experience with fetishism. The connection argued here between inhibitions and distortions in the sexual and intellectual realms suggests, as a domain for further inquiry, the possibility of a more general investigation into the role of sexual fantasies in intellectual activities.

History, 20th Century↗
PubMedDate not supplied

Mathematics and learning disabilities.

Between 5% and 8% of school-age children have some form of memory or cognitive deficit that interferes with their ability to learn concepts or procedures in one or more mathematical domains. A review of the arithmetical competencies of these children is provided, along with discussion of underlying memory and cognitive deficits and potential neural correlates. The deficits are discussed in terms of three subtypes of mathematics learning disability and in terms of a more general framework for linking research in mathematical cognition to research in learning disabilities.

Child↗
PubMedDate not supplied

Mathematics education in the United States: past to present.

This article presents a historical review of mathematics education since the late 1950s in the United States. Three themes are used to organize the literature reviewed in the article: (a) broad sociopolitical forces, particularly highly publicized educational policy statements; (b) trends in mathematics research; and (c) theories of learning and instruction. At times, these themes coincide, as was the case in the 1990s. In other cases, such as the recent push for educational accountability, these themes conflict. Nonetheless, the themes go a long way to explain the serpentine nature of reform in the United States over the last 45 years. This article also attempts to account for developments in special education as well as general education research, something that does not appear in most historical presentations of mathematics education.

History, 20th Century↗
PubMedDate not supplied

Early identification and interventions for students with mathematics difficulties.

This article highlights key findings from the small body of research on mathematics difficulties (MD) relevant to early identification and early intervention. The research demonstrates that (a) for many children, mathematics difficulties are not stable over time; (b) the presence of reading difficulties seems related to slower progress in many aspects of mathematics; (c) almost all students with MD demonstrate problems with accurate and automatic retrieval of basic arithmetic combinations, such as 6 + 3. The following measures appear to be valid and reliable indicators of potential MD in kindergartners: (a) magnitude comparison (i.e., knowing which digit in a pair is larger), (b) sophistication of counting strategies, (c) fluent identification of numbers, and (d) working memory (as evidenced by reverse digit span). These are discussed in terms of the components of number sense. Implications for early intervention strategies are explored.

Age Factors↗