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Results for “Mathematical Computing”

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PubMed2005

Mathematical modeling and computer simulation in blood coagulation.

Over the last two decades, mathematical modeling has become a popular tool in study of blood coagulation. The in silico methods were able to yield interesting and significant results in the understanding of both individual reaction mechanisms and regulation of large sections of the coagulation cascade. The objective of this paper is to review the development of theoretical research in hemostasis and thrombosis, to summarize the main findings, and outline problems and possible prospects in the use of mathematical modeling and computer simulation approaches. This review is primarily focused on the studies dealing with: (1) the membrane-dependent reactions of coagulation; (2) regulation of the coagulation cascade, including effects of positive and negative feedback loops, diffusion of coagulation factors, and blood flow.

Blood Coagulation↗

PubMed1994

Analyses of normal and abnormal esophageal transport using computer simulations.

Mathematical modeling and computer simulations are combined with concurrent manometric and videofluoroscopic data to analyze the contractile behavior of the esophageal wall during normal and abnormal esophageal bolus transport. The study focuses on axial variations in intraluminal pressure in relationship to deformations of the esophageal wall during the transport process. Four case studies of esophageal bolus transport described by Kahrilas et al. (Gastroenterology 94: 73-80, 1988), one normal and three abnormal, are analyzed in detail by capturing the major elements of both the videofluoroscopic and concurrent manometric data in the mathematical model. In all cases a strong correlation between the deformations of the luminal wall and the axial variations of intraluminal pressure is observed. Simulation of normal bolus transport shows that, whereas only gentle variations in intrabolus pressure occur in the main body of the bolus due to weak frictional forces there, large frictional forces force a rapid rise in pressure near the bolus tail induced by circular muscle squeeze. Of particular interest is the analysis of incomplete clearance of bolus fluid in the aortic arch region. The only physically correct model consistent both with the videofluoroscopic and the manometric data implies the existence of two separate contraction waves, one above and one below the transition zone.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗

PubMed2002

A strategy to enhance the usability of the minimal model as used with the intravenous glucose tolerance test in diabetes research and clinical management.

The Minimal Model method of determining Insulin Sensitivity from the Intravenous glucose Tolerance Test is a valuable tool for the Diabetes research community. However the Minimal Model algorithm itself is not readily available in a user-friendly modem windows environment to the clinical researcher in many research departments. In addition use of the model often requires intervention by an experienced "modeller" to interpret the results produced by the method. This paper proposes a more readily available and usable version of the program and discusses the issues which surround the use of the program by clinical researchers without computer mathematical modelling experience.

Algorithms↗

PubMed1999

A computational model for tracking subsurface tissue deformation during stereotactic neurosurgery.

Recent advances in the field of stereotactic neurosurgery have made it possible to coregister preoperative computed tomography (CT) and magnetic resonance (MR) images with instrument locations in the operating field. However, accounting for intraoperative movement of brain tissue remains a challenging problem. While intraoperative CT and MR scanners record concurrent tissue motion, there is motivation to develop methodologies which would be significantly lower in cost and more widely available. The approach we present is a computational model of brain tissue deformation that could be used in conjunction with a limited amount of concurrently obtained operative data to estimate subsurface tissue motion. Specifically, we report on the initial development of a finite element model of brain tissue adapted from consolidation theory. Validations of the computational mathematics in two and three dimensions are shown with errors of 1%-2% for the discretizations used. Experience with the computational strategy for estimating surgically induced brain tissue motion in vivo is also presented. While the predicted tissue displacements differ from measured values by about 15%, they suggest that exploiting a physics-based computational framework for updating preoperative imaging databases during the course of surgery has considerable merit. However, additional model and computational developments are needed before this approach can become a clinical reality.

Animals↗

PubMed1991

[Automated diagnosis of vibration disease].

Based on a multidimensional discriminant analysis of the clinical and physiological characteristics derived as a result of examination of 593 miners, classification functions were plotted, allowing the diagnosis of vibratory disease in the automatic mode by means of mathematic computations. Functional indicators of skin sensitivity, particularly vibratory, dynamometry, rheovasography and thermography of the hand and fingers, a "white spot" symptom, and characteristics derived on a mathematic analysis of heart rhythm were established to be informative for automated diagnosis. The diagnosis was found to be more accurate in case of using a two-stage variant of the discriminant analysis where the differentiation is first made between healthy workers and workers with a pathology, followed by the discrimination of the preclinical and clinical phase of the disease. The automated diagnostic system is demonstrated to compare very favourably with the conventional method of diagnosis.

Arctic Regions↗

PubMed1991

Modeling and simulation in biomedicine.

A group of researchers and educators in The Netherlands, Germany and Czechoslovakia have developed and adapted mathematical computer models of phenomena in the field of physiology and biomedicine for use in higher education. The models are graphical and highly interactive, and are all written in TurboPascal or the mathematical simulation language PSI. An educational shell has been developed to launch the models. The shell allows students to interact with the models and teachers to edit the models, to add new models and to monitor the achievements of the students. The models and the shell have been implemented on a MS-DOS personal computer. This paper describes the features of the modeling package and presents the modeling and simulation of the heart muscle as an example.

Computer Graphics↗

PubMed1997

[The mathematical modelling and computation of the stressed-deformed state of metal-ceramic dentures].

The SPLEN-K (INZOMA) computing system, based on the mathematical model of a heterogeneous elastic body with linear plastic reinforcement helps estimate the design of coated dentures with due consideration for the individual features of the jaws and teeth, articulation, and occlusion. The open module type of this system permits its modifications and improvements, allows introduction of individual changes in the planned denture design, helps rapidly estimate the changes in the strained-deformed state and assess the correctness of the result from the computed data. The reliability of estimations was assessed in special tests. Practical results of theoretical studies are adequate to clinical and experimental data.

Computer Simulation↗

PubMed1980

Computer simulation: a diagnostic method in comparative studies of valve prostheses.

Computer simulation was used to compare flow characteristics through Starr-Edwards and Björk-Shiley valves in the mitral and aortic positions. Pressure and velocity determinations were mathematically computed with the use of a model based on the recognition that blood is a non-Newtonian fluid. The results were displayed in two-dimensional graphic form. In both the mitral and aortic positions the Björk-Shiley prosthesis showed a more favorable laminar flow pattern, producing fewer eddies and smaller pressure and velocity gradients through the occluder. Computer simulation is a valuable adjunct in the comparative testing of the hemodynamic properties of artificial heart valves and offers several advantages over physical simulators.

Aortic Valve↗

PubMed1997

K-TEA Mathematics scores of learning disabled students in resource and inclusive settings.

The relative effectiveness of mathematics instruction in resource rooms versus inclusive settings was examined with 30 boys in Grades 5 and 6 identified as learning disabled in mathematics. The boys were presented at the beginning of the school year and posttested at the end. Treatment was 45 min. of daily instruction in mathematics provided by six teachers for one school year. K-TEA Mathematics Computation and Application scores, separately compared in 2 x 2 repeated measures analyses of variance, were not significantly different; however, a significant gain was noted across settings for K-TEA Mathematics Application scores.

Achievement↗

PubMed1994

Numerical simulation of propagating concentration profiles in renal tubules.

Method-dependent mechanisms that may affect dynamic numerical solutions of a hyperbolic partial differential equation that models concentration profiles in renal tubules are described. Some numerical methods that have been applied to the equation are summarized, and ways by which the methods may misrepresent true solutions are analysed. Comparison of these methods demonstrates the need for thoughtful application of computational mathematics when simulating complicated time-dependent phenomena.

Artifacts↗

PubMed1999

Diagnostic in normal pressure hydrocephalus: A mathematical model for determination of the ICP-dependent resistance and compliance.

The internationally accepted calculation methods concerning cerebrospinal fluid dynamics proceed from a pressure independent resistance to cerebrospinal fluid outflow. In a new model we focus our attention on the pressure dependency of resistance. In our calculation model we are monitoring the complete pressure course p(t) over the time during and after the infusion. The comparison of the pressure rise On(p) during the infusion and the descent Off(p) after the infusion at the same pressure level allows one to construct all formulas for the compliance C(p) and resistance R(p). The computerized analysis of the results of the intrathecal infusion test using our mathematical computation leads to a simplification of this investigation. The simultaneous measurement of the resistance and compliance during a single investigation allows one to minimize the patient's discomfort. In contrast to the classical methods it is not necessary that the ICP reaches a plateau. Our mathematical method diverges with the description of a pressure dependent slope of the function for the resistance from the static examination models. For that we are able to take the non-linearity of the cerebrospinal fluid resorption into consideration.

Computer Simulation↗

PubMed1994

A comparison of test procedures for multidose animal carcinogenicity assays under competing risks.

Four multidose animal carcinogenicity assay trend test procedures based on the chi-square, Hoel-Walburg, log-rank, and Peto procedures are compared under conditions of competing risks. A total of 42 different risk populations are simulated in which a simulated animal can contract one or more of five different tumor types. The risk populations contain such different risks as incidence of tumor increasing with dose, time of death increasing or decreasing with dose, tumor decreasing time of death without necessarily causing death (nonrepresentativeness), and combinations of the above. Each population is analyzed using each of the four procedures for linear dose-response effect for each tumor separately and for all animals with tumors. Results show the Peto procedure to be the most robust of the four, giving rejection rates near the nominal for all competing risk situations and having the best power to reject when rejection is called for.

Animals↗

PubMed1979

RADIONUCLIDE COMPUTED TOMOGRAPHY: APPLICATIONS IN CARDIOVASCULAR DISEASE.

Tomography is an imaging modality in which information in one plane is displayed in focus while information from overlying and underlying planes is either blurred or eliminated. As a result, there is an improvement in the contrast of structures in the plane of interest. Computerized axial tomography (CAT) is an imaging modality in which a digital computer mathematically reconstructs the image of a plane or section from data collected perpendicular to the axis of that plane. The axis of the plane and the patient's long axis usually coincide so that the reconstructed images reveal transverse sections. In recent years, two types of computed tomography in medical imaging have generated a great deal of interest. These are X-ray transmission and radio-nuclide emission computed tomography.

Journal Article↗

PubMedDate not supplied

[The mathematical modelling of the displacement of the hard palate tissues in conservative uranoplasty].

Presents a mathematical model of sparing uranoplasty techniques developed by the authors; using this model, a physician may assess before surgery the volume of tissues needed to close the palatal defect. Experience gained with 72 surgeries carried out in children with unilateral cleft palate confirms the desirability of preliminary computations. Mathematical models for the most prevalent sparing uranoplasty methods are offered.

Child↗

PubMed1989

Using mathematical programming to assess the relative performance of the health care industry.

Unlike conventional methods for evaluating program efficiency, a recently developed mathematical programming technique, Data Envelopment Analysis (DEA), is able to handle multiple inputs and outputs simultaneously without assigning arbitrary weights and does not require the use of homogeneous measurement units nor a prespecified functional relationship between inputs and outputs. Despite of its unfamiliarity to health care researchers and administrators, this technique is becoming increasingly popular as a means of evaluating relative performance in not-for-profit entities.

Decision Making, Organizational↗

PubMed1997

Mathematical formulation for computing the performance of self expanding helical stents.

Stents are cylindrical devices implanted inside pathologic tubular passages within the body. The stents, which are made of metal or plastic, keep the passage open for flow (of blood, urine, air etc.) by applying radial pressure on the passage walls. In most cases the stents are selected empirically for each application. We introduce here a mathematical formula for computing the radial pressure induced by self expanding helical stents. The formula was verified experimentally for an urological stent using a special device. The results correlate well with the theoretical predictions (R = 0.997; y = 1.017 x -0.06 kg; SEE = 0.034, for forces and R = 0.9988; y = 1.04 x +8.7 mmHg; SEE = 25.3 for pressures). This formula can potentially serve as an analytical tool for selecting the most suitable stent for a given application.

Angioplasty, Balloon, Coronary↗

PubMed2001

A mathematical algorithm that computes breast cancer sizes and doubling times detected by screening.

This paper presents a mathematical algorithm that computes the sizes and growth rates of breast cancer detected in a hypothetical population that is screened for the disease. The algorithm works by simulating the outcomes of the hypothetical population twice, first without screening and then with screening. The simulation without screening relies on an underlying model of the natural history of the disease. The simulation with screening uses this natural history model to track the growth of breast tumors backwards in the time starting from the time they would have been detected without screening. The method of tracking tumor growth backward in time is different from methods that track tumor growth forward in time by starting from an estimated time of tumor onset. The screening algorithm combines the natural history model, the method tracking of tumor growth backward in time, the age group, the interval between screening exams, and the detection threshold of the screening exam to compute the joint distribution of tumor size and growth rate among screen-detected and interval patients. The algorithm also computes the sensitivity and leadtime distribution. It allows for arbitrary age groups, detection thresholds and screening intervals and may contribute to the design of future screening trials.

Age Factors↗

PubMed1985

A mathematical model and computer program for adriamycin distribution and elimination.

A mathematical physiological flow model is described for the distribution and elimination of adriamycin in the rat. The model includes the volume or mass of, and blood flow to the following tissues: heart, plasma, muscle, skin, kidney, bone marrow, gut, liver and bile. A compartment is also included for tight or almost irreversible binding which occurs with this drug. The program was written in FORTRAN to compute the concentration of drug in each tissue as a function of time after bolus injection or short term infusion. The computed data is printed on a line printer and recorded on disk for use in a SAS program GPLOT to obtain precision plots.

Animals↗