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 1,081 records · Page 60Linked to original sources
PubMedDate not supplied

A Mathematical simulation to explain the coordinated functions of efflux and metabolism limiting the transport of anti-HIV agents across Caco-2 cells.

OBJECTIVES: The purpose of this study was to simulate a mathematical model that explains the coordinated function of P-glycoprotein (P-gp) and/or CYP3A4 in human intestinal enterocytes. In addition, this study aimed to determine the efflux interactions of anti-HIV protease inhibitors. METHODS: Human colon carcinoma-derived Caco-2 cells were selected as a model system to evaluate the effects of P-gp-mediated efflux of HIV protease inhibitors. Anti-HIV agents ritonavir and saquinavir were selected as model drugs to determine efflux interactions. An absorption-metabolism classification system is hence proposed based on substrate specificities of drugs toward P-gp and/or CYP3A4 and their probable interactions with other compounds. RESULTS: Enhanced apical to basal (A-B) ritonavir transport was observed on coadministration of saquinavir. Saturable, concentration-dependent inhibition of ritonavir efflux from Caco-2 monolayers was also observed with saquinavir. The IC(50) values of ritonavir (as a self-inhibitor) and saquinavir from dose-response curves, estimated by fitting the data to nonlinear equations, were found to be 7.15 and 33.2 micromol/L, respectively. The respective K(i) values determined were 8.5 and 28.91 micromol/L. The experimentally obtained K(i) values decreased in the close approximation with the IC(50) values. CONCLUSION: Proposed mathematical simulations may prove to be a useful tool in predicting drug interactions by inhibition of P-gp mediated efflux and CYP3A4-mediated metabolism.

ATP Binding Cassette Transporter, Subfamily B, Mem↗
PubMed2006

Mathematical calculation of pedicle subtraction osteotomy size to allow precision correction of fixed sagittal deformity.

STUDY DESIGN: This is a retrospective review of 15 consecutive fixed sagittal plane deformity patients who have undergone pedicle subtraction osteotomies. The focus of this article is the application of a trigonometric equation that calculates the degree of correction needed to achieve sagittal balance. The intraoperative predictive accuracy and clinical radiographic results of using this mathematical equation are discussed. OBJECTIVE: The need for a precise and reproducible planning tool for the correction of sagittal imbalance prompted us to apply a simple trigonometric equation to achieve the desired sagittal alignment of the spine. SUMMARY OF BACKGROUND DATA: Establishing sagittal balance has been widely recognized as one of the most important parameters in optimizing outcomes for spinal reconstruction patients. Preoperative planning for sagittal plane correction in adult spinal deformity has traditionally been done by estimation or with cumbersome film cutouts. To our knowledge, there has not been a consistent method of calculating the exact number of degrees needed to reestablish spinal balance. METHODS: Patients' C7 plumb lines are measured on a 36-inch radiograph to assess the degree of sagittal imbalance and determine how many degrees of correction (and subsequent millimeters of wedge resection) are needed. Applying a basic trigonometric formula for the tangent to the sagittal alignment is used to do this. RESULTS: We have used this technique reliably in a series of 15 consecutive patients to reestablish sagittal balance. The predicted degree of correction was compared to the achieved degree of correction at the site of the osteotomy. This comparison was accurate to within 3 degrees (the standard error of measurement for the method of Cobb) in all cases except 2. CONCLUSIONS: By using a simple mathematical equation, one can reliably determine the degree of pedicle subtraction osteotomy needed for correction of sagittal deformity. This technique is reproducible and has led to successful clinical outcomes.

Adult↗
PubMed2004

Expiratory trigger setting in pressure support ventilation: from mathematical model to bedside.

OBJECTIVE: To evaluate the feasibility of relying on a mathematical model to adjust the optimal level of expiratory trigger, materialized by the ratio of inspiratory flow at the end of inspiratory effort (V'ti) and peak inspiratory flow (V'peak), or V'ti/V'peak, during pressure support, by comparing its predicted values with those measured in intubated patients. DESIGN: Prospective observational study. SETTING: Medical intensive care unit, university hospital. PATIENTS: There were 28 intubated patients undergoing pressure support. INTERVENTIONS: Pressure support as set by the clinician in charge. MEASUREMENTS AND MAIN RESULTS: A significant correlation was found between predicted and measured V'ti/V'peak ratios (r =.70; p <.001; mean +/- sd difference, -0.025 +/- 0.07; 95% confidence interval, -0.161 to 0.111). Overall, delayed cycling occurred in obstructive conditions, the delay increasing as obstructive disease was more severe. CONCLUSIONS: A significant correlation was observed between predicted values of V'ti/V'peak and those values measured in patients undergoing pressure support. These findings should stimulate further research into the possible applications of this mathematical model to optimize expiratory trigger setting. Furthermore, our findings suggest that expiratory trigger should be adjustable and provide a wider range of cutoff levels than that which is currently available.

Feasibility Studies↗
PubMed2004

Mathematical models of the acute inflammatory response.

PURPOSE OF REVIEW: Trauma and infection elicit an acute inflammatory response. In certain circumstances the degree of the acute inflammatory response may result in pathologic manifestations, namely, sepsis and multiple organ failure. Despite an extensive series of clinical trials designed to modulate inflammation in sepsis, only one compound, activated protein C, has emerged from more than 250 failed trials. There is a growing recognition that the complexity of the acute inflammatory response precludes the efficient development of therapies for sepsis and multiple organ failure until systems approaches are brought to bear on this problem. RECENT FINDINGS: Work carried out by the authors' groups suggests that mathematical modeling can provide a means by which in vitro and in vivo data can be synthesized into system-level analytic models of the acute inflammatory response. The authors have focused on agent-based modeling and modeling with ordinary differential equations. Some of the advantages and disadvantages of these modeling approaches are presented, and methods for calibration and validation of these models are discussed. Finally, the usefulness of mathematical models to evaluate the prospective therapeutic strategies in clinical trials of sepsis and trauma is examined. SUMMARY: Simulations using various methods can shed insight into the pathophysiology of the acute inflammatory response and may lead to better design of clinical trials in sepsis and trauma.

Acute Disease↗
PubMed2006

The role of initial trauma in the host's response to injury and hemorrhage: insights from a correlation of mathematical simulations and hepatic transcriptomic analysis.

Trauma and hemorrhagic shock (HS) elicit severe physiological disturbances that predispose the victims to subsequent organ dysfunction and death. The general lack of effective therapeutic options for these patients is mainly due to the complex interplay of interacting inflammatory and physiological elements working at multiple levels. Systems biology has emerged as a new paradigm that allows the study of large portions of physiological networks simultaneously. Seeking a better understanding of the interplay among known inflammatory pathways, we constructed a mathematical model encompassing the dynamics of the acute inflammatory response that incorporates the intertwined effects of inflammation and global tissue damage. The model was calibrated using data from C57Bl/6 mice subjected to endotoxemia, sham operation (i.e., surgical trauma induced by cannulation [ST]) or ST + HS+ resuscitation (ST-HS-R). An in silico simulation, made at whole-organism level, suggested that similar pathways of different magnitudes were operant as the degree of total body damage increased. We sought to validate this hypothesis by subjecting mice to HS and comparing the models predictions to circulating markers of inflammation and tissue injury as well as the global transcriptomic response of the liver. C57Bl/6 mice were subjected to ST or ST-HS (without resuscitation). Liver gene expression was assessed using an Affymetrix DNA microarray (GeneChip Mouse Expression Set 430A, Affymetrix, Santa Clara, CA), which contains 22,621 probe sets and effectively interrogates 12,341 mouse genes. The microarray data sets were subjected to hierarchical clustering and pathway analysis. In agreement with model predictions, circulating levels of inflammation/tissue injury markers and the microarray analysis both demonstrated that ST alone accounts for a substantial proportion of the observed phenotypic and genetic/molecular changes versus untreated animals. The addition of HS further increased the magnitude of gene expression, but relatively few additional genes were recruited. Mathematical simulations and DNA microarrays, both systems biology tools, may provide valuable insight into the complex global physiological interactions that occur in response to trauma and hemorrhagic shock.

Animals↗
PubMed2006

A mathematical model of pacemaker activity recorded from mouse small intestine.

The pacemaker activity of interstitial cells of Cajal (ICCs) has been known to initiate the propagation of slow waves along the whole gastrointestinal tract through spontaneous and repetitive generation of action potentials. We studied the mechanism of the pacemaker activity of ICCs in the mouse small intestine and tested it using a mathematical model. The model includes ion channels, exchanger, pumps and intracellular machinery for Ca2+ regulation. The model also incorporates inositol 1,4,5-triphosphate (IP3) production and IP3-mediated Ca2+ release activities. Most of the parameters were obtained from the literature and were modified to fit the experimental results of ICCs from mouse small intestine. We were then able to compose a mathematical model that simulates the pacemaker activity of ICCs. The model generates pacemaker potentials regularly and repetitively as long as the simulation continues. The frequency was set at 20 min(-1) and the duration at 50% repolarization was 639 ms. The resting and overshoot potentials were -78 and +1.2 mV, respectively. The reconstructed pacemaker potentials closely matched those obtained from animal experiments. The model supports the idea that cyclic changes in [Ca2+]i and [IP3] play key roles in the generation of ICC pacemaker activity in the mouse small intestine.

Action Potentials↗
PubMed1974

Effect of Noise on the Mathematical Parameters that Describe Isothermal Seed Germination.

A mathematical model is proposed to describe the isothermal germination rate of seeds as a function of time. All environmental parameters were held constant with the exception of the sound-pressure level and the frequency of the impinging sound waves. Each single frequency sound has its own set of mathematical parameters that describe the differential germination rate as a function of time. Frequencies of 100, 1000, 2000, 4000, and 9000 hertz as well as broad band noise, all at 100 decibels, were used in the experiments.

Journal Article↗
PubMed1999

Graph-set analysis of hydrogen-bond patterns: some mathematical concepts.

To provide a foundation for further theoretical and software development of the application of graph sets to patterns of hydrogen bonding and other intermolecular interactions a number of mathematical concepts and tools are defined, developed and demonstrated. Following a review of the basic definitions and uses of graph sets, the directional properties of hydrogen bonds are now included in the treatment. The concepts of a constructor graph and covalent distance matrix have been developed to aid in the generation of a qualitative descriptor for the straightforward, consistent and ultimately automatic (with appropriate software) definition of patterns. An additional mathematical tool, the arrowed T-labeling, has been developed to deal with situations in which pattern-forming moieties are located on crystallographic special positions. To demonstrate the utility and various features of these concepts they are applied in detail to two particular structures, polymorphic iminodiacetic acid [N-(carboxymethyl)glycine] and trans-tetraamminedinitrocobalt(III) acetate. To facilitate the application and use of graph sets many of these developments have already been incorporated into the software of the Cambridge Structural Database, as described in the accompanying paper.

Journal Article↗
PubMed1989

Optimal insulin infusion resulting from a mathematical model of blood glucose dynamics.

Mathematical optimization techniques are applied to a simplified mathematical model of blood glucose dynamics to derive insulin infusion programs for the control of blood glucose levels in diabetic individuals. Two particular cases are discussed. First, the insulin infusion program which results in an initially high blood glucose level being reduced to acceptable levels. Second, the control of blood glucose levels following a meal, prior to which blood glucose and net blood-glycemic hormone were at their fasting levels.

Blood Glucose↗
PubMed2005

Application of a generalized MWC model for the mathematical simulation of metabolic pathways regulated by allosteric enzymes.

In our effort to elucidate the systems biology of the model organism, Escherichia coli, we have developed a mathematical model that simulates the allosteric regulation for threonine biosynthesis pathway starting from aspartate. To achieve this goal, we used kMech, a Cellerator language extension that describes enzyme mechanisms for the mathematical modeling of metabolic pathways. These mechanisms are converted by Cellerator into ordinary differential equations (ODEs) solvable by Mathematica. In this paper, we describe a more flexible model in Cellerator, which generalizes the Monod, Wyman, Changeux (MWC) model for enzyme allosteric regulation to allow for multiple substrate, activator and inhibitor binding sites. Furthermore, we have developed a model that describes the behavior of the bifunctional allosteric enzyme aspartate Kinase I-Homoserine Dehydrogenase I (AKI-HDHI). This model predicts the partition of enzyme activities in the steady state which paves a way for a more generalized prediction of the behavior of bifunctional enzymes.

Algorithms↗
PubMed2004

A mathematical model for breast cancer lesion estimation: electrical impedance technique using TS2000 commercial system.

We present a mathematical model to analyze transadmittance data for the detection of breast cancer using TransScan TS2000 commercial system. The model was constructed based on the assumption that a lesion exists near the surface of a breast region. The breast region that is considered as a background is assumed to be homogeneous at least near the surface where we attach a planar array of electrodes. Based on the model, we developed a lesion estimation algorithm utilizing single- or multifrequency transadmittance data. The approximate ratio of two conductivity values for the lesion and background needs to be known to estimate the size of the lesion even though the location estimate does not require this ratio. From the results of numerical simulations with added noise, we suggest better ways of interpreting TS2000 transadmittance images for the detection of breast cancer with improved accuracy. Since this study provides a rigorous mathematical modeling of TS2000 commercial system, it will be possible to apply the technique to lesion estimation problems based on more realistic models of breast regions in future studies.

Breast Neoplasms↗
PubMed2005

A mathematical analysis of SFAP convolutional models.

In this paper we compare, from a mathematical point of view, two well-recognized single fiber action potential (SFAP) convolutional models: the Nandedkar-Stalberg (N-S) model and the Dimitrov-Dimitrova (D-D) model. Junction waves appear in N-S SFAPs due to the onset and extinction of the monopoles whereas in D-D SFAPs these waves appear only when the dipoles reach the fiber/tendon junctions. D-D junction waves model more accurately the out-of-the-main-spike waveforms that appear in experimental SFAPs. The origin of junction waves lies in the discontinuities of the impulse responses. There are two kinds of these waves caused by the two types of existing discontinuities (in the impulse response function and in its derivative). We model each kind of discontinuity with a different mathematical function. Using these functions, the N-S and D-D impulse responses can be split and, therefore, the junction waves can be separated from the spike component of the SFAP. The expansion of the impulse response helps us to understand the differences between the N-S and D-D junction waves.

Action Potentials↗
PubMed2002

Mathematical generation of normal data for evaluating myocardial perfusion studies.

In this paper, we present a new mathematical method that synthesizes normal data sets for quantification of regional myocardium perfusion. In clinical practice, regional myocardial perfusion is often measured with a gamma camera and quantified via circumferential profile analysis. Normal reference profile data is used to increase the accuracy of the clinical interpretations. Our goal is to create reference data from an existing set of archived studies. An iterative mathematical method, based on two statistical hypotheses, was used to generate the study set instead of collecting normal examinations from a healthy population. Clinical validation is based on interpretations by six independent observers. Results of evaluation with synthesized normal data and its validation are presented.

Algorithms↗
PubMed2005

Selective photothermolysis of blood vessels following flashlamp-pumped pulsed dye laser irradiation: in vivo results and mathematical modelling are in agreement.

Laser therapy using the pulsed dye laser is the standard treatment for port-wine stains (PWS). But the mechanism of action has not been elucidated completely, yet. The dorsal skin-fold chamber model in hamsters was used to investigate the effects of laser treatment (lambda(em)=585 nm; pulse duration: 0.45 ms; fluence: 6 J per cm2) on blood vessels. Vessels (n=3394) were marked with FITC dextran (MW 150 kDa) and diameters (2-186 microm) were measured using intravital fluorescence microscopy up to 24 h following irradiation. Histology (H&E, TUNEL, CD31) was taken 1 or 24 h after irradiation. The experimental results were compared with the predictions of a mathematical model based on the finite-element method. Following irradiation treatment the number of unperfused vessels decreases with decreasing vessel diameter in vivo. Histology indicated a restriction of tissue injury to the irradiated area after 1 h. Blood vessels contained aggregated red blood cells. After 24 h tissue damage occurred also outside the irradiated area and thrombus formation was visible. These results were in agreement with the mathematical calculations. In addition to initial physical effects after pulsed dye laser treatment delayed biological processes contribute significantly to the reduction of perfused blood vessels. Because of incomplete photocoagulation of smaller blood vessels (diameter 2-16 microm) a complete bleaching of PWS seems to be unlikely.

Animals↗
PubMed2004

Mathematical methods in combatting terrorism.

This document is a preliminary report on the role that mathematical and statistical methods might play in the defense against terrorist attacks. In no way does this replace the efforts of law enforcement agencies or intelligence activities. The hope is that mathematical techniques can make their efforts more efficient. The ideas enumerated here utilize the notion of probabilistic risk analysis, which was developed for the purpose of assessing the safety of nuclear reactors, as well as randomization and game theory. More extensive work in these directions is contemplated for the future. The author is planning workshops to evaluate the ideas presented here and to elicit additional methodologies that may prove useful in this endeavor.

Journal Article↗
PubMed1992

Epidemiology, HIV and drugs: mathematical models and data.

The utility of mathematical models in understanding the dynamics of HIV transmission among injecting drug users (IDUs) and their non-IDU sex partners is discussed. We emphasize the need for collaborative relationships between modellers and drug-use researchers, and we stress that models should be based on data in both their formulation and development stages. We outline some of the possible data requirements of transmission models and we highlight the need for the collection of appropriate quantitative data, so that modellers can estimate specific parameters for their models. We believe that discussion of the needs and utility of mathematical modelling will lead to mutually beneficial collaborations between theoreticians and drug-use researchers. These collaborations may aid in the design and the evaluation of effective behavioural or medical intervention strategies.

England↗
PubMed1990

Mathematical model analysis of mouse epidermal cell kinetics measured by bivariate DNA/anti-bromodeoxyuridine flow cytometry and continuous [3H]-thymidine labelling.

In a previous study the epidermal cell kinetics of hairless mice were investigated with bivariate DNA/anti-bromodeoxyuridine (BrdU) flow cytometry of isolated basal cells after BrdU pulse labelling. The results confirmed our previous observations of two kinetically distinct sub-populations in the G2 phase. However, the results also showed that almost all BrdU-positive cells had left S phase 6-12 h after pulse labelling, contradicting our previous assumption of a distinct, slowly cycling, major sub-population in S phase. The latter study was based on an experiment combining continuous tritiated thymidine [( 3H]TdR) labelling and cell sorting. The purpose of the present study was to use a mathematical model to analyse epidermal cell kinetics by simulating bivariate DNA/BrdU data in order to get more details about the kinetic organization and cell cycle parameter values. We also wanted to re-evaluate our assumption of slowly cycling cells in S phase. The mathematical model shows a good fit to the experimental BrdU data initiated either at 08.00 hours or 20.00 hours. Simultaneously, it was also possible to obtain a good fit to our previous continuous labelling data without including a sub-population of slowly cycling cells in S phase. This was achieved by improving the way in which the continuous [3H]TdR labelling was simulated. The presence of two distinct subpopulations in G2 phase was confirmed and a similar kinetic organization with rapidly and slowly cycling cells in G1 phase is suggested. The sizes of the slowly cycling fractions in G1 and G2 showed the same distinct circadian dependency. The model analysis indicates that a small fraction of BrdU labelled cells (3-5%) was arrested in G2 phase due to BrdU toxicity. This is insignificant compared with the total number of labelled cells and has a negligible effect on the average cell cycle data. However, it comprises 1/3 to 1/2 of the BrdU positive G2 cells after the pulse labelled cells have been distributed among the cell cycle compartments.

Animals↗
PubMed2005

Assessment of Cottle's areas through the application of a mathematical model deriving from acoustic rhinometry and rhinomanometric data.

OBJECTIVES: Each nasal area, as defined by Cottle, has a different influence on the nasal airflow. The longitudinal distribution of resistances in nasal cavities was calculated by the anterior rhinomanometry and acoustic rhinometry data. DESIGN: Dynamic study of Cottle's areas in normal subjects was carried out by rhinomanometry and acoustic rhinometry. SETTING: Study by the Department of Otolaryngology of the University of Rome-La Sapienza. PARTICIPANTS: Twenty-seven Caucasian adults in local and general healthy conditions took part and completed this study, with a total of 54 nasal cavities included because of negativity at ENT-examination and clinical history, with normal respiratory parameters at the rhinomanometry and acoustic rhinometry. MAIN OUTCOME MEASURES: We determined nasal and acoustic resistances, nasal volumes and cross-sectional surface areas, as defined by Cottle, using nasal endoscopy. The longitudinal distribution of nasal resistances was obtained by integrating experimental surface areas using a novel mathematical model. The estimation of the longitudinal nasal resistance variations as a result of a theoretical reduction of the surface areas. RESULTS: The reduction of the 2-3-1 areas (in this order of importance) showed the greatest influence on the nasal resistances with coefficients of determinations greater than 0.98, this being quite different from that of the areas 4 and 5 for quite smaller area reduction percentages. CONCLUSIONS: The areas 2-3-1 control the overall nasal resistance so the surgical procedures on these areas greatly influence the dynamics of nasal airflow. The mathematical model developed here gives useful information to nasal functional surgery and may be applied to other schemes of nasal cavity.

Acoustics↗