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PubMed1982

Fluid dynamics of the mitral valve: physiological aspects of a mathematical model.

This paper presents a computational method that can be used to study the fluid computational method that can be used to study the fluid dynamics of the natural or prosthetic mitral valve in a computer test chamber with contractile muscular walls that model the left side of the heart. Having solved the equations of motion and predicted the performance of the valve, the computer presents the results in terms of flow patterns (streamlines), pressure-contour plots, and graphs of velocity, pressure, flow, tension, and distance as functions of time. Predicted echocardiograms and phonocardiograms are also generated by the computer. These predictions are compared with the results of animal experiments, and the method is used to study the diastolic role of the chordae tendineae, the pathophysiology of mitral valve prolapse syndrome, and the fluid dynamics of pivoting disc valves. Our results support the hypothesis that the chordae have a functional role during diastole. The results also establish a computer model of mitral prolapse, which should be useful in functional studies of that condition, and show that the position of the pivot point and the curvature of the occluder can have a profound effect on the angle of opening of pivoting disc valves. These studies illustrate the applications of the method in physiology, pathophysiology, and prosthetic valve design.

Animals↗
PubMed1991

A mathematical model for the computation of carboxyhaemoglobin in human blood as a function of exposure time.

A mathematical model is developed for the carbon monoxide (CO) uptake by the blood by taking into account the molecular diffusion, convection, facilitated diffusion and the non-equilibrium kinetics of CO with haemoglobin. The overall rate for the combination of CO with haemoglobin is derived by including the dissociation of CO from carboxyhaemoglobin (COHb). The resulting coupled system of nonlinear partial differential equation with physiologically relevant initial, entrance and boundary conditions is solved numerically. A fixed point iterative technique is used to deal with nonlinearities. The concentration of COHb in the blood is computed as a function of exposure time and ambient CO concentration. The COHb levels computed from our model are in good agreement with those measured experimentally. Also, results computed from our model give better approximation to the experimental values compared with the results from other models. The time taken by the blood COHb to attain 95% of its equilibrium value is computed. The COHb concentration in the blood increases with the increase in ventilation rate, association rate coefficient of CO with haemoglobin and total haemoglobin content in the blood, and with the decrease in dissociation rate coefficient of CO with haemoglobin and mean capillary blood PO2. It is found that the COHb level in the blood is not affected significantly because of endogenous production of CO in the body under normal condition. However, the effect may be significant in the patients with haemolytic anaemia.

Capillaries↗
PubMed2005

A study of fitness distance correlation as a difficulty measure in genetic programming.

We present an approach to genetic programming difficulty based on a statistical study of program fitness landscapes. The fitness distance correlation is used as an indicator of problem hardness and we empirically show that such a statistic is adequate in nearly all cases studied here. However, fitness distance correlation has some known problems and these are investigated by constructing an artificial landscape for which the correlation gives contradictory indications. Although our results confirm the usefulness of fitness distance correlation, we point out its shortcomings and give some hints for improvement in assessing problem hardness in genetic programming.

Algorithms↗
PubMed1988

Mathematical means to allow computer calculation of stereotaxic settings.

Stereotaxic instruments have wide use in neuroscience research. In certain of these machines the electrode can be introduced at an angle as well as perpendicularly. Computation of instrument settings to place the electrode in the desired location is the problem this paper addresses. Mathematical formulae are presented that allow a computer to calculate instrument settings given coordinates and angles read from a stereotaxic atlas.

Animals↗
PubMed2006

Membrane computing: brief introduction, recent results and applications.

The internal organization and functioning of living cells, as well as their cooperation in tissues and higher order structures, can be a rich source of inspiration for computer science, not fully exploited at the present date. Membrane computing is an answer to this challenge, well developed at the theoretical (mathematical and computability theory) level, already having several applications (via usual computers), but without having yet a bio-lab implementation. After briefly discussing some general issues related to natural computing, this paper provides an informal introduction to membrane computing, focused on the main ideas, the main classes of results and of applications. Then, three recent achievements, of three different types, are briefly presented, with emphasis on the usefulness of membrane computing as a framework for devising models of interest for biological and medical research.

Algorithms↗
PubMed1993

Vertical transport of radiocesium in surface soils: model implementation and dose-rate computation.

A mathematical model on the Radionuclide Behaviour in Soil for the study of the migration of radionuclides in undisturbed soil profile has been developed. The model has been calibrated using 134Cs and 137Cs concentrations along soil samples gathered in a natural grassland and beech wood, respectively, located in the Friuli-Venezia Giulia region (northeastern part of Italy). In these sampling sites, the external exposure due to 134Cs and 137Cs distribution along the soil profile has been also assessed.

Accidents↗
PubMed1990

Effect on a cariogenic challenge of saliva/plaque exchange via a thin salivary film studied by mathematical modelling.

Computer models can be powerful tools for studying complex interacting processes. The computer model of events in dental plaque during a cariogenic challenge described here simulates diffusion and metabolism of substrate, plus coupled diffusion/reaction of fourteen other species, charged and uncharged, including acidic metabolic products and fixed buffers. Its extension to deal with the effects of poor contact with bulk saliva when the plaque is presumed covered by a thin salivary film is here considered. Site-specific mixing rates between film and salivary pool were modelled phenomenologically, using data from the literature. Fast mixing was assumed during an initial carbohydrate intake phase (2 min sugar rinse), followed by site-dependent mixing and logarithmic clearance. The analysis also suggested a possible way of estimating local salivary film thickness. Increasing the halving time for exchange between film and bulk saliva was shown to prolong the pH minimum greatly, and to increase mineral loss. The respective roles of fixed buffers as stores of protons and of mobile buffers (especially bicarbonate) as exporters of protons from the inner plaque were emphasised.

Buffers↗
PubMed2002

Optimization of background electrolytes for capillary electrophoresis: II. Computer simulation and comparison with experiments.

A mathematical and computational model described in the previous paper (Gas, B., Coufal, P., Jaros, M., Muzikár, J., Jelínek, L., J. Chromatogr. A 2001, 905, 269-279) is adapted, algorithmized, and a computer program PeakMaster having a status of freeware (http://natur.cuni.cz/ approximately gas) is introduced. The model enables optimization of background electrolyte (BGE) systems for capillary zone electrophoresis. The model allows putting to use uni- or di- or trivalent electrolytes and allows also for modeling highly acidic or alkaline BGEs. It takes into account the dependence of ionic mobilities and dissociation of weak electrolytes on the ionic strength. The model calculates the effective mobility of analytes and predicts parameters of the system that are experimentally available, such as the transfer ratio, which is a measure of the sensitivity in the indirect UV detection or the molar conductivity detection response, which expresses the sensitivity of the conductivity detection. Further, the model enables evaluation of a tendency of the analyte to undergo electromigration dispersion or peak broadening. The suitability of the model is verified by comparison of the predicted results with experiments, even under conditions that are far from ideal (under extreme pH and a high ionic strength).

Algorithms↗
PubMed2005

Impact of virtual tumor resection and computer-assisted risk analysis on operation planning and intraoperative strategy in major hepatic resection.

HYPOTHESIS: Currently, standard planning for hepatic resection is based on the schematic description of the functional anatomy of the liver according to Couinaud, and on the evaluation of 2-dimensional computed tomographic imaging of the liver. Recent developments in image-based computer assistance allow patients' individual functional liver anatomy to be computed from mathematical analysis of standard multidetector computed tomographic scans. An intended resection can be performed virtually under realistic anatomic conditions, and the influence of different resection planes on blood supply and drainage within the remaining liver parenchyma can be calculated by a computer-assisted risk analysis. We evaluated the impact of computer-assisted risk analysis on operation planning for major hepatectomies, in particular on extent of resection or need for vascular reconstruction. DESIGN: Prospective cohort study. SETTING: Academic tertiary care referral center. PATIENTS: Twenty-five consecutive patients admitted to the hospital for major hepatectomy, of whom 4 had tumors deemed unresectable by both methods. INTERVENTIONS: Two-dimensional computed tomography was used to calculate the volume of the future liver remnant with the intended resection line manually determined, and then the volume of the future liver remnant was calculated again by computer-assisted risk analysis as the remaining liver volume not being devascularized but having both portal venous blood supply and hepatic venous drainage. MAIN OUTCOME MEASURES: The difference between the remaining functional liver volumes calculated by the 2 methods. RESULTS: The deviation between liver volumes determined by 2-dimensional computed tomography and by computer-assisted risk analysis was less than 20% in 14 of 21 patients, between 20% and 30% in 3, between 30% and 40% in 2, and 41% and 43% in 1 patient each. The most extensive deviations were found in extended left hepatectomy or when left hepatectomy was combined with additional wedge resection in the right lobe. In 7 cases, all with a deviation greater than 20%, the results of computer-assisted risk analysis led to a change of operation planning with regard to the extent of resection (n = 3) or the need for vascular reconstruction (n = 4), although in 1 of these cases resection was not performed because of peritoneal carcinomatosis. CONCLUSIONS: Image-based computer assistance allows for areas at risk for devascularization or venous congestion to be identified and precisely calculated before resection. In selected cases with small liver remnants, operation planning may be improved substantially by preoperative computer-assisted risk analysis.

Adult↗
PubMed1991

Thickness extrema at the edge of shaped lenses: the general problem and the solution for a straight edge obtained by means of direct elimination and of Lagrange multipliers.

In general thickness varies along the cut edge of a lens. There is some interest in being able to predict the locations of the thickest and thinnest points on the edge. One purpose of this paper was to formulate the general problem mathematically of finding the locations of thickness extrema on the edge of an arbitrary lens cut into an arbitrary shape. A second purpose was to illustrate how the problem can be solved. In particular, the problem is solved completely and explicitly for what is probably the simplest case, the straight cut edge. A component-free matrix expression for the position of the extremum is derived by employing Lagrange multipliers and the concept of the generalized inverse of a matrix. The equation applies to spheres, cylinders and sphero-cylinders and allows for the presence of prism as well. Along some edges the thickness is constant. Along other edges the thickness varies linearly; there are no extrema except for the practical extrema at the two ends of the edge: thickest at the one and thinnest at the other. The mathematical conditions for these two cases are presented. Equivalent to the matrix equation for the position vector of the thickness extremum is a pair of scalar equations expressed in terms of components of the matrices. The pair is useful when locating extrema using manual calculations. On the other hand, the component-free matrix equation is useful in other circumstances such as for mathematical manipulations and when using computer software that handles matrices. The former is used in a number of numerical examples; the latter was used to check the answers by computer. The mathematical techniques described here are likely to find application in other areas of ophthalmic and visual optics.

Lenses↗
PubMed1991

LSTSQ: a module for reliable constrained and unconstrained nonlinear regression.

A software module for nonlinear regression analysis, based on the reliable Meyer-Roth algorithm (a modified damped least square algorithm), is presented. It allows both constrained and unconstrained optimization, and the use of a variety of weighting methods. Virtually any nonlinear function can be fitted, including those with several nondependent variables. The package has been thoroughly tested, and is available in several common computer languages (Pascal, Modula-2 and C). It is easy to use, and advanced knowledge of mathematics or computers is not essential. Standard test problems, and a fully working example of use on enzyme kinetics are included.

Algorithms↗
PubMed1988

[Biomathematical approaches to the problems of radiation biology and medicine].

A vast experience in the introduction of modern mathematical methods into research activities of the Central Research Roentgenoradiology Institute was accumulated in the Department of Biomathematics. The Information-retrieval System for Storage and Analysis of Data on the Activities of X-ray Service in the USSR, a package of applied programs for statistical analysis of radiation therapy effectiveness, a controlled data base on 6 cancer sites, 2 systems for simulation of radiation effects on heterogeneous cell systems were worked out. Some priority results in the fields of mathematical biology and statistical analysis of incomplete selective data were obtained. The Department is heading the work on the problem "Mathematics and computer technology in radiobiology and radiation biophysics".

Humans↗